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Are purely-analog audio devices immune to aliasing?
Re: Are purely-analog audio devices immune to aliasing?
Earl Kiosterud wrote:
> Without pre-filtering, they'd have the very aliasing
> that digital systems can have.
But won't an analog device just smoothly cut-off a frequency that is too
high -- i.e. at a certain point the cut-off gradually beings and the
higher an incoming frequency is, the more it will be attenuated --
without any aliasing?
Earl Kiosterud wrote:
> Without pre-filtering, they'd have the very aliasing
> that digital systems can have.
But won't an analog device just smoothly cut-off a frequency that is too
high -- i.e. at a certain point the cut-off gradually beings and the
higher an incoming frequency is, the more it will be attenuated --
without any aliasing?
Re: Are purely-analog audio devices immune to aliasing?
Green Xenon [Radium] wrote:
> the cut-off gradually beings
Sorry that should read "the cut-off gradually *begins*"
Green Xenon [Radium] wrote:
> the cut-off gradually beings
Sorry that should read "the cut-off gradually *begins*"
Re: Are purely-analog audio devices immune to aliasing?
"Green Xenon [Radium]" <glucegen1@excite . com > wrote in message
news:48291e51$0$31745$4c368faf@roadrunner . com ...
> Green Xenon [Radium] wrote:
>
>
>> the cut-off gradually beings
>
>
> Sorry that should read "the cut-off gradually *begins*"
Radium,
An alias is a modulation product that we don't want -- one that appears in our passband.
Any modulation system produces various modulation products -- we just have to structure it
so that they don't wind up where we don't want them. The fact that we're doing
discrete-amplitude sampling (16-bit or whatever), has nothing to do with it -- it's the fact
that we're doing it in discrete time intervals (a form of amplitude modulation, based on a
carrier, like 44.1 KHz.).
The following is to illustrate the potential for aliases in an analog system, not to depict
how carrier systems were actually implemented.
Imagine it's the 60s, and you're building a telephone carrier system where you want to
translate a voice channel, 0-4KHz, to the 4-8KHz channel. So you modulate a 4 Khz sine-wave
carrier with your baseband audio. This produces sum and difference freqencies. The sum
frequencies fall right in the channel you want, 4-8KHz. For example, a 1 Khz baseband
(original audio) component produces 5 Khz in your channel, exactly as you want. 2 KHz
produces 6 KHz, etc. The difference frequencies fall in the 4-zero KHz range, looking like
upside down audio. For example, 1 Khz of baseband produces 3 Khz. That's OK, because
you're going to filter the after-modulation signal (post-filter) for only 4-8KHz. If you
don't, you'll have adjacent-channel interference, as Don points out in his reply.
Similarly, the sum-frequency products of baseband signals above 4 KHz would wind up above 8
KHz, messing up other channels (i.e.: 5 KHz would wind up at 9 KHz, messing up the 8-12KHz
channel). More adjacent-channel interference.
Now imagine a 9KHz baseband component. It would wind up at 5 KHz -- smack in the middle of
your channel, but at a different frequency. These things don't sound pretty. Your
post-filtering would not remove it, because it's in your channel. That's an alias. So you
must filter your baseband (before modulation, or pre-filtering) below 8 KHz to prevent this
alias from being generated. In reality, you'd probably have pre-filtered your baseband from
0-4KHz anyway.
My point is that there was no sampling, just pure simple sine-carrier analog amplitude
modulation, and we still have the potential for aliases. The theory is the same, whether
it's digital (discrete) or plain old garden-variety analog amplitude modulation.
Also, you can see that there's no inherent cutoff in such analog systems, as you asked
about. You have to provide it to prevent aliases and modulation artifacts from winding up
in your audio.
Now you didn't ask about this, but since I'm this far, I'll take this to the digital world
of CD audio. If the baseband were not pre-filtered below Nyquist (22.05 KHz) before
sampling, then e.g.: a 24 KHz audio component would appear as 19.9 Khz. (44.1 KHz - 24 Khz).
That'd also be an alias -- a simple difference product. The higher the baseband is allowed
to creep above Nyquist, the more alias junk we hear creeping downwards into the audio band,
mirrored around the Nyquist frequency. We must filter the baseband to below Nyquist to
prevent aliases, and similarly post filter the sampled signal to prevent those sum and
difference signals around 44.1 KHz from appearing with our recovered audio. We wouldn't
hear it, but it'd give our amplifiers and speakers stuff to deal with unnecessarily.
--
Earl
"Green Xenon [Radium]" <glucegen1@excite . com > wrote in message
news:48291e51$0$31745$4c368faf@roadrunner . com ...
> Green Xenon [Radium] wrote:
>
>
>> the cut-off gradually beings
>
>
> Sorry that should read "the cut-off gradually *begins*"
Radium,
An alias is a modulation product that we don't want -- one that appears in our passband.
Any modulation system produces various modulation products -- we just have to structure it
so that they don't wind up where we don't want them. The fact that we're doing
discrete-amplitude sampling (16-bit or whatever), has nothing to do with it -- it's the fact
that we're doing it in discrete time intervals (a form of amplitude modulation, based on a
carrier, like 44.1 KHz.).
The following is to illustrate the potential for aliases in an analog system, not to depict
how carrier systems were actually implemented.
Imagine it's the 60s, and you're building a telephone carrier system where you want to
translate a voice channel, 0-4KHz, to the 4-8KHz channel. So you modulate a 4 Khz sine-wave
carrier with your baseband audio. This produces sum and difference freqencies. The sum
frequencies fall right in the channel you want, 4-8KHz. For example, a 1 Khz baseband
(original audio) component produces 5 Khz in your channel, exactly as you want. 2 KHz
produces 6 KHz, etc. The difference frequencies fall in the 4-zero KHz range, looking like
upside down audio. For example, 1 Khz of baseband produces 3 Khz. That's OK, because
you're going to filter the after-modulation signal (post-filter) for only 4-8KHz. If you
don't, you'll have adjacent-channel interference, as Don points out in his reply.
Similarly, the sum-frequency products of baseband signals above 4 KHz would wind up above 8
KHz, messing up other channels (i.e.: 5 KHz would wind up at 9 KHz, messing up the 8-12KHz
channel). More adjacent-channel interference.
Now imagine a 9KHz baseband component. It would wind up at 5 KHz -- smack in the middle of
your channel, but at a different frequency. These things don't sound pretty. Your
post-filtering would not remove it, because it's in your channel. That's an alias. So you
must filter your baseband (before modulation, or pre-filtering) below 8 KHz to prevent this
alias from being generated. In reality, you'd probably have pre-filtered your baseband from
0-4KHz anyway.
My point is that there was no sampling, just pure simple sine-carrier analog amplitude
modulation, and we still have the potential for aliases. The theory is the same, whether
it's digital (discrete) or plain old garden-variety analog amplitude modulation.
Also, you can see that there's no inherent cutoff in such analog systems, as you asked
about. You have to provide it to prevent aliases and modulation artifacts from winding up
in your audio.
Now you didn't ask about this, but since I'm this far, I'll take this to the digital world
of CD audio. If the baseband were not pre-filtered below Nyquist (22.05 KHz) before
sampling, then e.g.: a 24 KHz audio component would appear as 19.9 Khz. (44.1 KHz - 24 Khz).
That'd also be an alias -- a simple difference product. The higher the baseband is allowed
to creep above Nyquist, the more alias junk we hear creeping downwards into the audio band,
mirrored around the Nyquist frequency. We must filter the baseband to below Nyquist to
prevent aliases, and similarly post filter the sampled signal to prevent those sum and
difference signals around 44.1 KHz from appearing with our recovered audio. We wouldn't
hear it, but it'd give our amplifiers and speakers stuff to deal with unnecessarily.
--
Earl
Re: Are purely-analog audio devices immune to aliasing?
"Earl Kiosterud" <someone@nowhere . com > wrote in message news:ipiWj.342$lj.202@trnddc01...
> "Green Xenon [Radium]" <glucegen1@excite . com > wrote in message
> news:48291e51$0$31745$4c368faf@roadrunner . com ...
>> Green Xenon [Radium] wrote:
>>
>>
>>> the cut-off gradually beings
>>
>>
>> Sorry that should read "the cut-off gradually *begins*"
>
> Radium,
>
> An alias is a modulation product that we don't want -- one that appears in our passband.
> Any modulation system produces various modulation products -- we just have to structure it
> so that they don't wind up where we don't want them. The fact that we're doing
> discrete-amplitude sampling (16-bit or whatever), has nothing to do with it -- it's the
> fact that we're doing it in discrete time intervals (a form of amplitude modulation, based
> on a carrier, like 44.1 KHz.).
>
> The following is to illustrate the potential for aliases in an analog system, not to
> depict how carrier systems were actually implemented.
>
> Imagine it's the 60s, and you're building a telephone carrier system where you want to
> translate a voice channel, 0-4KHz, to the 4-8KHz channel. So you modulate a 4 Khz
> sine-wave carrier with your baseband audio. This produces sum and difference freqencies.
> The sum frequencies fall right in the channel you want, 4-8KHz. For example, a 1 Khz
> baseband (original audio) component produces 5 Khz in your channel, exactly as you want.
> 2 KHz produces 6 KHz, etc. The difference frequencies fall in the 4-zero KHz range,
> looking like upside down audio. For example, 1 Khz of baseband produces 3 Khz. That's
> OK, because you're going to filter the after-modulation signal (post-filter) for only
> 4-8KHz. If you don't, you'll have adjacent-channel interference, as Don points out in his
> reply. Similarly, the sum-frequency products of baseband signals above 4 KHz would wind up
> above 8 KHz, messing up other channels (i.e.: 5 KHz would wind up at 9 KHz, messing up the
> 8-12KHz channel). More adjacent-channel interference.
>
> Now imagine a 9KHz baseband component. It would wind up at 5 KHz -- smack in the middle
> of your channel, but at a different frequency. These things don't sound pretty. Your
> post-filtering would not remove it, because it's in your channel. That's an alias. So
> you must filter your baseband (before modulation, or pre-filtering) below 8 KHz to prevent
> this alias from being generated. In reality, you'd probably have pre-filtered your
> baseband from 0-4KHz anyway.
>
> My point is that there was no sampling, just pure simple sine-carrier analog amplitude
> modulation, and we still have the potential for aliases. The theory is the same, whether
> it's digital (discrete) or plain old garden-variety analog amplitude modulation.
>
> Also, you can see that there's no inherent cutoff in such analog systems, as you asked
> about. You have to provide it to prevent aliases and modulation artifacts from winding up
> in your audio.
>
> Now you didn't ask about this, but since I'm this far, I'll take this to the digital world
> of CD audio. If the baseband were not pre-filtered below Nyquist (22.05 KHz) before
> sampling, then e.g.: a 24 KHz audio component would appear as 19.9 Khz. (44.1 KHz - 24
> Khz). That'd also be an alias -- a simple difference product. The higher the baseband is
> allowed to creep above Nyquist, the more alias junk we hear creeping downwards into the
> audio band, mirrored around the Nyquist frequency. We must filter the baseband to below
> Nyquist to prevent aliases, and similarly post filter the sampled signal to prevent those
> sum and difference signals around 44.1 KHz from appearing with our recovered audio. We
> wouldn't hear it, but it'd give our amplifiers and speakers stuff to deal with
> unnecessarily.
> --
> Earl
>
It occurs to me that I'm going to catch some flak for using the term "alias" in non-sampled
systems. I think the more correct terms are "image" and "mirror." But "alias" is used
interchangeably, it seems. Bottom line: you have the same problems. It doesn't sound as
ignorant as "RMS Power," but the idea is similar. It ain't right, but we know what we
mean.
--
Earl
"Earl Kiosterud" <someone@nowhere . com > wrote in message news:ipiWj.342$lj.202@trnddc01...
> "Green Xenon [Radium]" <glucegen1@excite . com > wrote in message
> news:48291e51$0$31745$4c368faf@roadrunner . com ...
>> Green Xenon [Radium] wrote:
>>
>>
>>> the cut-off gradually beings
>>
>>
>> Sorry that should read "the cut-off gradually *begins*"
>
> Radium,
>
> An alias is a modulation product that we don't want -- one that appears in our passband.
> Any modulation system produces various modulation products -- we just have to structure it
> so that they don't wind up where we don't want them. The fact that we're doing
> discrete-amplitude sampling (16-bit or whatever), has nothing to do with it -- it's the
> fact that we're doing it in discrete time intervals (a form of amplitude modulation, based
> on a carrier, like 44.1 KHz.).
>
> The following is to illustrate the potential for aliases in an analog system, not to
> depict how carrier systems were actually implemented.
>
> Imagine it's the 60s, and you're building a telephone carrier system where you want to
> translate a voice channel, 0-4KHz, to the 4-8KHz channel. So you modulate a 4 Khz
> sine-wave carrier with your baseband audio. This produces sum and difference freqencies.
> The sum frequencies fall right in the channel you want, 4-8KHz. For example, a 1 Khz
> baseband (original audio) component produces 5 Khz in your channel, exactly as you want.
> 2 KHz produces 6 KHz, etc. The difference frequencies fall in the 4-zero KHz range,
> looking like upside down audio. For example, 1 Khz of baseband produces 3 Khz. That's
> OK, because you're going to filter the after-modulation signal (post-filter) for only
> 4-8KHz. If you don't, you'll have adjacent-channel interference, as Don points out in his
> reply. Similarly, the sum-frequency products of baseband signals above 4 KHz would wind up
> above 8 KHz, messing up other channels (i.e.: 5 KHz would wind up at 9 KHz, messing up the
> 8-12KHz channel). More adjacent-channel interference.
>
> Now imagine a 9KHz baseband component. It would wind up at 5 KHz -- smack in the middle
> of your channel, but at a different frequency. These things don't sound pretty. Your
> post-filtering would not remove it, because it's in your channel. That's an alias. So
> you must filter your baseband (before modulation, or pre-filtering) below 8 KHz to prevent
> this alias from being generated. In reality, you'd probably have pre-filtered your
> baseband from 0-4KHz anyway.
>
> My point is that there was no sampling, just pure simple sine-carrier analog amplitude
> modulation, and we still have the potential for aliases. The theory is the same, whether
> it's digital (discrete) or plain old garden-variety analog amplitude modulation.
>
> Also, you can see that there's no inherent cutoff in such analog systems, as you asked
> about. You have to provide it to prevent aliases and modulation artifacts from winding up
> in your audio.
>
> Now you didn't ask about this, but since I'm this far, I'll take this to the digital world
> of CD audio. If the baseband were not pre-filtered below Nyquist (22.05 KHz) before
> sampling, then e.g.: a 24 KHz audio component would appear as 19.9 Khz. (44.1 KHz - 24
> Khz). That'd also be an alias -- a simple difference product. The higher the baseband is
> allowed to creep above Nyquist, the more alias junk we hear creeping downwards into the
> audio band, mirrored around the Nyquist frequency. We must filter the baseband to below
> Nyquist to prevent aliases, and similarly post filter the sampled signal to prevent those
> sum and difference signals around 44.1 KHz from appearing with our recovered audio. We
> wouldn't hear it, but it'd give our amplifiers and speakers stuff to deal with
> unnecessarily.
> --
> Earl
>
It occurs to me that I'm going to catch some flak for using the term "alias" in non-sampled
systems. I think the more correct terms are "image" and "mirror." But "alias" is used
interchangeably, it seems. Bottom line: you have the same problems. It doesn't sound as
ignorant as "RMS Power," but the idea is similar. It ain't right, but we know what we
mean.
--
Earl
Re: Are purely-analog audio devices immune to aliasing?
Earl Kiosterud wrote:
> "Green Xenon [Radium]" <glucegen1@excite . com > wrote in message
> news:4828deb3$0$5698$4c368faf@roadrunner . com ...
>> Hi:
>>
>> Is it true that purely-analog audio devices [such as analog cassette, AM radio, and the
>> pre-digital telephone systems*] are immune to aliasing?
>>
>> *By pre-digital telephone systems, I am referring to how these systems operated prior to
>> using digital technology. Nowadays, many analog phone systems do use DSP somewhere along
>> the line. Similar applies to the analog AM radio, it used to be just analog but now it
>> utilizes some amount of DSP indirectly.
>>
>> Thanks,
>>
>> Radium
>
> The pre-digital telephone system used frequency-division multiplexing, each voice channel in
> a 4 KHz slot. Nyquist was 4 KHz. Without pre-filtering, they'd have the very aliasing
> that digital systems can have. Without post-filtering, you'd hear sidebands around 8 KHz.
> No difference, except the sampling frequency.
No that isn't aliasing, it is adjacent channel interference - a totally
different thing. Aliasing is a product of sampling, an ambiguation of
the signal caused by the fact that it is sampled at discrete points and
whatever is in between those points must be filled in with assumptions
about its nature. In audio, the assumption is generally that the signal
between those points contains the lowest possible frequency solution
below the Nyquist frequency. But the other solutions, involving higher
frequencies are equally valid from a mathematical point of view - they
are the alias solutions.
d
Earl Kiosterud wrote:
> "Green Xenon [Radium]" <glucegen1@excite . com > wrote in message
> news:4828deb3$0$5698$4c368faf@roadrunner . com ...
>> Hi:
>>
>> Is it true that purely-analog audio devices [such as analog cassette, AM radio, and the
>> pre-digital telephone systems*] are immune to aliasing?
>>
>> *By pre-digital telephone systems, I am referring to how these systems operated prior to
>> using digital technology. Nowadays, many analog phone systems do use DSP somewhere along
>> the line. Similar applies to the analog AM radio, it used to be just analog but now it
>> utilizes some amount of DSP indirectly.
>>
>> Thanks,
>>
>> Radium
>
> The pre-digital telephone system used frequency-division multiplexing, each voice channel in
> a 4 KHz slot. Nyquist was 4 KHz. Without pre-filtering, they'd have the very aliasing
> that digital systems can have. Without post-filtering, you'd hear sidebands around 8 KHz.
> No difference, except the sampling frequency.
No that isn't aliasing, it is adjacent channel interference - a totally
different thing. Aliasing is a product of sampling, an ambiguation of
the signal caused by the fact that it is sampled at discrete points and
whatever is in between those points must be filled in with assumptions
about its nature. In audio, the assumption is generally that the signal
between those points contains the lowest possible frequency solution
below the Nyquist frequency. But the other solutions, involving higher
frequencies are equally valid from a mathematical point of view - they
are the alias solutions.
d
Re: Are purely-analog audio devices immune to aliasing?
Hi Don,
Suppose we set up an amplitude-modulation system using a multiplier, except that we reverse
the carrier (44.1 KHz) and the baseband audio. We offset the 44.1 KHz signal (so it is
always positive) but not the baseband -- it's allowed to operate in two quadrants of our
multiplier. You could say that the carrier is modulating the baseband, instead of the usual
other way around. The resulting signal would include the baseband components, and a set of
AM sidebands around 44.1KHz, images of the audio components, just as with CD audio (except
there wouldn't be sidebands around 88.2 KHz, 132.3 KHz., etc). If we allow our audio to go
past 22.05 Khz, we'll have spurious stuff in our baseband frequency range. For example, an
audio component at 30 KHz would produce a component at 14.1 Khz.
Isn't that the same spurious component (same frequency) we'd get with aliasing in the case
of CD audio? This system is continuous (the audio isn't sampled -- it's allowed to change
continuously), yet we have a sort of a Nyquist frequency under which our baseband must stay
in order to not get signal components in our output that are ambiguous.
--
Earl
"Don Pearce" <nospam@nospam . com > wrote in message
news:9K2dnS2KKdBNgLTVnZ2dnUVZ8rCdnZ2d@plusnet...
> Earl Kiosterud wrote:
>> "Green Xenon [Radium]" <glucegen1@excite . com > wrote in message
>> news:4828deb3$0$5698$4c368faf@roadrunner . com ...
>>> Hi:
>>>
>>> Is it true that purely-analog audio devices [such as analog cassette, AM radio, and the
>>> pre-digital telephone systems*] are immune to aliasing?
>>>
>>> *By pre-digital telephone systems, I am referring to how these systems operated prior to
>>> using digital technology. Nowadays, many analog phone systems do use DSP somewhere along
>>> the line. Similar applies to the analog AM radio, it used to be just analog but now it
>>> utilizes some amount of DSP indirectly.
>>>
>>> Thanks,
>>>
>>> Radium
>>
>> The pre-digital telephone system used frequency-division multiplexing, each voice channel
>> in a 4 KHz slot. Nyquist was 4 KHz. Without pre-filtering, they'd have the very
>> aliasing that digital systems can have. Without post-filtering, you'd hear sidebands
>> around 8 KHz. No difference, except the sampling frequency.
>
> No that isn't aliasing, it is adjacent channel interference - a totally different thing.
> Aliasing is a product of sampling, an ambiguation of the signal caused by the fact that it
> is sampled at discrete points and whatever is in between those points must be filled in
> with assumptions about its nature. In audio, the assumption is generally that the signal
> between those points contains the lowest possible frequency solution below the Nyquist
> frequency. But the other solutions, involving higher frequencies are equally valid from a
> mathematical point of view - they are the alias solutions.
>
> d
Hi Don,
Suppose we set up an amplitude-modulation system using a multiplier, except that we reverse
the carrier (44.1 KHz) and the baseband audio. We offset the 44.1 KHz signal (so it is
always positive) but not the baseband -- it's allowed to operate in two quadrants of our
multiplier. You could say that the carrier is modulating the baseband, instead of the usual
other way around. The resulting signal would include the baseband components, and a set of
AM sidebands around 44.1KHz, images of the audio components, just as with CD audio (except
there wouldn't be sidebands around 88.2 KHz, 132.3 KHz., etc). If we allow our audio to go
past 22.05 Khz, we'll have spurious stuff in our baseband frequency range. For example, an
audio component at 30 KHz would produce a component at 14.1 Khz.
Isn't that the same spurious component (same frequency) we'd get with aliasing in the case
of CD audio? This system is continuous (the audio isn't sampled -- it's allowed to change
continuously), yet we have a sort of a Nyquist frequency under which our baseband must stay
in order to not get signal components in our output that are ambiguous.
--
Earl
"Don Pearce" <nospam@nospam . com > wrote in message
news:9K2dnS2KKdBNgLTVnZ2dnUVZ8rCdnZ2d@plusnet...
> Earl Kiosterud wrote:
>> "Green Xenon [Radium]" <glucegen1@excite . com > wrote in message
>> news:4828deb3$0$5698$4c368faf@roadrunner . com ...
>>> Hi:
>>>
>>> Is it true that purely-analog audio devices [such as analog cassette, AM radio, and the
>>> pre-digital telephone systems*] are immune to aliasing?
>>>
>>> *By pre-digital telephone systems, I am referring to how these systems operated prior to
>>> using digital technology. Nowadays, many analog phone systems do use DSP somewhere along
>>> the line. Similar applies to the analog AM radio, it used to be just analog but now it
>>> utilizes some amount of DSP indirectly.
>>>
>>> Thanks,
>>>
>>> Radium
>>
>> The pre-digital telephone system used frequency-division multiplexing, each voice channel
>> in a 4 KHz slot. Nyquist was 4 KHz. Without pre-filtering, they'd have the very
>> aliasing that digital systems can have. Without post-filtering, you'd hear sidebands
>> around 8 KHz. No difference, except the sampling frequency.
>
> No that isn't aliasing, it is adjacent channel interference - a totally different thing.
> Aliasing is a product of sampling, an ambiguation of the signal caused by the fact that it
> is sampled at discrete points and whatever is in between those points must be filled in
> with assumptions about its nature. In audio, the assumption is generally that the signal
> between those points contains the lowest possible frequency solution below the Nyquist
> frequency. But the other solutions, involving higher frequencies are equally valid from a
> mathematical point of view - they are the alias solutions.
>
> d
Re: Are purely-analog audio devices immune to aliasing?
On Thu, 15 May 2008 15:42:44 GMT, "Earl Kiosterud"
<someone@nowhere . com > wrote:
>Hi Don,
>
>Suppose we set up an amplitude-modulation system using a multiplier, except that we reverse
>the carrier (44.1 KHz) and the baseband audio. We offset the 44.1 KHz signal (so it is
>always positive) but not the baseband -- it's allowed to operate in two quadrants of our
>multiplier. You could say that the carrier is modulating the baseband, instead of the usual
>other way around. The resulting signal would include the baseband components, and a set of
>AM sidebands around 44.1KHz, images of the audio components, just as with CD audio (except
>there wouldn't be sidebands around 88.2 KHz, 132.3 KHz., etc). If we allow our audio to go
>past 22.05 Khz, we'll have spurious stuff in our baseband frequency range. For example, an
>audio component at 30 KHz would produce a component at 14.1 Khz.
>
>Isn't that the same spurious component (same frequency) we'd get with aliasing in the case
>of CD audio? This system is continuous (the audio isn't sampled -- it's allowed to change
>continuously), yet we have a sort of a Nyquist frequency under which our baseband must stay
>in order to not get signal components in our output that are ambiguous.
>--
>Earl
Let me think about this! I'll do the maths later. I think you are
right that you will get stuff all over the place that you don't want,
but I think I would tend to call them images rather than aliases.
I also suspect that the use of a synchronous demodulator might let you
recover the signals (as you can recover modulation over 100% this
way), meaning that the signals aren't truly jumbled - they just appear
that way. Aliasing is truly there for ever once it happens - there is
no way back.
OK, let me change my mind. I've just used Mathcad to look at this. I
made two FFT spectra - one with 44.1k as the carrier and 3k as the
modulation and the other with 3k as the carrier and 44.1k as the
modulation.
For the first I see a carrier at 44.1kHz, and sidebands at 41.1 and
47.1kHz. Exactly as you expect.
For the second I see a carrier at 3kHz and sidebands at 44.1 and
47.1kHz. Which is exactly as you expect once you know what to expect
;-)
Which will do for me. It would even be a nice way to generate
suppressed carrier AM - just filter away the 3kHz when done
modulating.
d
--
Pearce Consulting
* w w w .pearce.uk . com
On Thu, 15 May 2008 15:42:44 GMT, "Earl Kiosterud"
<someone@nowhere . com > wrote:
>Hi Don,
>
>Suppose we set up an amplitude-modulation system using a multiplier, except that we reverse
>the carrier (44.1 KHz) and the baseband audio. We offset the 44.1 KHz signal (so it is
>always positive) but not the baseband -- it's allowed to operate in two quadrants of our
>multiplier. You could say that the carrier is modulating the baseband, instead of the usual
>other way around. The resulting signal would include the baseband components, and a set of
>AM sidebands around 44.1KHz, images of the audio components, just as with CD audio (except
>there wouldn't be sidebands around 88.2 KHz, 132.3 KHz., etc). If we allow our audio to go
>past 22.05 Khz, we'll have spurious stuff in our baseband frequency range. For example, an
>audio component at 30 KHz would produce a component at 14.1 Khz.
>
>Isn't that the same spurious component (same frequency) we'd get with aliasing in the case
>of CD audio? This system is continuous (the audio isn't sampled -- it's allowed to change
>continuously), yet we have a sort of a Nyquist frequency under which our baseband must stay
>in order to not get signal components in our output that are ambiguous.
>--
>Earl
Let me think about this! I'll do the maths later. I think you are
right that you will get stuff all over the place that you don't want,
but I think I would tend to call them images rather than aliases.
I also suspect that the use of a synchronous demodulator might let you
recover the signals (as you can recover modulation over 100% this
way), meaning that the signals aren't truly jumbled - they just appear
that way. Aliasing is truly there for ever once it happens - there is
no way back.
OK, let me change my mind. I've just used Mathcad to look at this. I
made two FFT spectra - one with 44.1k as the carrier and 3k as the
modulation and the other with 3k as the carrier and 44.1k as the
modulation.
For the first I see a carrier at 44.1kHz, and sidebands at 41.1 and
47.1kHz. Exactly as you expect.
For the second I see a carrier at 3kHz and sidebands at 44.1 and
47.1kHz. Which is exactly as you expect once you know what to expect
;-)
Which will do for me. It would even be a nice way to generate
suppressed carrier AM - just filter away the 3kHz when done
modulating.
d
--
Pearce Consulting
* w w w .pearce.uk . com
Re: Are purely-analog audio devices immune to aliasing?
"Don Pearce" <nospam@nospam . com > wrote in message news:482e5bea.25475953@news.plus . net ...
(snip)
>
> Let me think about this! I'll do the maths later. I think you are
> right that you will get stuff all over the place that you don't want,
> but I think I would tend to call them images rather than aliases.
>
> I also suspect that the use of a synchronous demodulator might let you
> recover the signals (as you can recover modulation over 100% this
> way), meaning that the signals aren't truly jumbled - they just appear
> that way. Aliasing is truly there for ever once it happens - there is
> no way back.
>
> OK, let me change my mind. I've just used Mathcad to look at this. I
> made two FFT spectra - one with 44.1k as the carrier and 3k as the
> modulation and the other with 3k as the carrier and 44.1k as the
> modulation.
>
> For the first I see a carrier at 44.1kHz, and sidebands at 41.1 and
> 47.1kHz. Exactly as you expect.
>
> For the second I see a carrier at 3kHz and sidebands at 44.1 and
> 47.1kHz. Which is exactly as you expect once you know what to expect
> ;-)
>
> Which will do for me. It would even be a nice way to generate
> suppressed carrier AM - just filter away the 3kHz when done
> modulating.
>
> d
>
>
> --
> Pearce Consulting
> * w w w .pearce.uk . com
Hey Don,
Here's how I see this. In your first case, the 41.1K and 47.1 K components are sidebands of
the 44.1K carrier. In the second case those same components are the (folded) sidebands (or
negative-frequency, which is perfectly valid)) of a 3 KHz carrier. The result is the
same -- they're the same sum and difference frequencies -- they don't really care who's
modulating whom! :) A sum frequency is a sum, and a difference is a difference. The only
real difference is if you add 0 Hz (DC offset) to either the audio or to the carrier. In
the case of the former, you get the 44.1K carrier component as well as the sidebands around
it, and in the latter you get baseband audio as well as the same sidebands around 44.1K.
And that's the result of the sum and difference frequencies too. Ain't no getting away from
it!
You mentioned generating suppressed-carrier generation, by filtering out the 3K component.
I think you can just multiply the signal with the baseband, adding 0 Hz (DC) to neither, and
get that. You have to use a four-quadrant multiplier (handles both negative and positive
signals). You should get no carrier and no baseband in the output -- just the sidebands.
ATSC TV adds a little DC to get a little bit of carrier (if I understand it correctly, and
I'm not at all sure I do) for recovery. At least that's one way of implementing it.
Forgive my excess of clarification comments in all this -- I don't mean to be pedantic, but
I try to be as clear as possible, and I think they might be useful to some of those who
might be following this thread.
The terms "mirror" and "image," I think, at least as used in superhet radio, refer to such
things as a modulation product that is the sum frequency, where only the difference was
wanted. It's a mirror around the local oscillator frequency. But in a more general sense,
any modulation product that winds up in your frequency band of interest (audio, in our case)
is an ambiguous component, in that we can't distinguish it from a real signal component.
I've always thought of any as an alias.
Here's my main thrust: I think the aliases we get in sampled audio where the audio goes
above Nyquist are simply the difference modulation products, which creep into our baseband
if the audio goes above Nyquist. As the audio gets higher in frequency, the sidebands get
lower, from 44.1K. Nyquist is simply the midpoint, where they meet. Sampling is a case of
general modulation theory.
Hoping to hear your comments.
--
Regards from Virginia Beach,
Earl
"Don Pearce" <nospam@nospam . com > wrote in message news:482e5bea.25475953@news.plus . net ...
(snip)
>
> Let me think about this! I'll do the maths later. I think you are
> right that you will get stuff all over the place that you don't want,
> but I think I would tend to call them images rather than aliases.
>
> I also suspect that the use of a synchronous demodulator might let you
> recover the signals (as you can recover modulation over 100% this
> way), meaning that the signals aren't truly jumbled - they just appear
> that way. Aliasing is truly there for ever once it happens - there is
> no way back.
>
> OK, let me change my mind. I've just used Mathcad to look at this. I
> made two FFT spectra - one with 44.1k as the carrier and 3k as the
> modulation and the other with 3k as the carrier and 44.1k as the
> modulation.
>
> For the first I see a carrier at 44.1kHz, and sidebands at 41.1 and
> 47.1kHz. Exactly as you expect.
>
> For the second I see a carrier at 3kHz and sidebands at 44.1 and
> 47.1kHz. Which is exactly as you expect once you know what to expect
> ;-)
>
> Which will do for me. It would even be a nice way to generate
> suppressed carrier AM - just filter away the 3kHz when done
> modulating.
>
> d
>
>
> --
> Pearce Consulting
> * w w w .pearce.uk . com
Hey Don,
Here's how I see this. In your first case, the 41.1K and 47.1 K components are sidebands of
the 44.1K carrier. In the second case those same components are the (folded) sidebands (or
negative-frequency, which is perfectly valid)) of a 3 KHz carrier. The result is the
same -- they're the same sum and difference frequencies -- they don't really care who's
modulating whom! :) A sum frequency is a sum, and a difference is a difference. The only
real difference is if you add 0 Hz (DC offset) to either the audio or to the carrier. In
the case of the former, you get the 44.1K carrier component as well as the sidebands around
it, and in the latter you get baseband audio as well as the same sidebands around 44.1K.
And that's the result of the sum and difference frequencies too. Ain't no getting away from
it!
You mentioned generating suppressed-carrier generation, by filtering out the 3K component.
I think you can just multiply the signal with the baseband, adding 0 Hz (DC) to neither, and
get that. You have to use a four-quadrant multiplier (handles both negative and positive
signals). You should get no carrier and no baseband in the output -- just the sidebands.
ATSC TV adds a little DC to get a little bit of carrier (if I understand it correctly, and
I'm not at all sure I do) for recovery. At least that's one way of implementing it.
Forgive my excess of clarification comments in all this -- I don't mean to be pedantic, but
I try to be as clear as possible, and I think they might be useful to some of those who
might be following this thread.
The terms "mirror" and "image," I think, at least as used in superhet radio, refer to such
things as a modulation product that is the sum frequency, where only the difference was
wanted. It's a mirror around the local oscillator frequency. But in a more general sense,
any modulation product that winds up in your frequency band of interest (audio, in our case)
is an ambiguous component, in that we can't distinguish it from a real signal component.
I've always thought of any as an alias.
Here's my main thrust: I think the aliases we get in sampled audio where the audio goes
above Nyquist are simply the difference modulation products, which creep into our baseband
if the audio goes above Nyquist. As the audio gets higher in frequency, the sidebands get
lower, from 44.1K. Nyquist is simply the midpoint, where they meet. Sampling is a case of
general modulation theory.
Hoping to hear your comments.
--
Regards from Virginia Beach,
Earl
Re: Are purely-analog audio devices immune to aliasing?
On Thu, 15 May 2008 21:38:09 GMT, "Earl Kiosterud"
<someone@nowhere . com > wrote:
>
>
>"Don Pearce" <nospam@nospam . com > wrote in message news:482e5bea.25475953@news.plus . net ...
>(snip)
>>
>> Let me think about this! I'll do the maths later. I think you are
>> right that you will get stuff all over the place that you don't want,
>> but I think I would tend to call them images rather than aliases.
>>
>> I also suspect that the use of a synchronous demodulator might let you
>> recover the signals (as you can recover modulation over 100% this
>> way), meaning that the signals aren't truly jumbled - they just appear
>> that way. Aliasing is truly there for ever once it happens - there is
>> no way back.
>>
>> OK, let me change my mind. I've just used Mathcad to look at this. I
>> made two FFT spectra - one with 44.1k as the carrier and 3k as the
>> modulation and the other with 3k as the carrier and 44.1k as the
>> modulation.
>>
>> For the first I see a carrier at 44.1kHz, and sidebands at 41.1 and
>> 47.1kHz. Exactly as you expect.
>>
>> For the second I see a carrier at 3kHz and sidebands at 44.1 and
>> 47.1kHz. Which is exactly as you expect once you know what to expect
>> ;-)
>>
>> Which will do for me. It would even be a nice way to generate
>> suppressed carrier AM - just filter away the 3kHz when done
>> modulating.
>>
>> d
>>
>>
>> --
>> Pearce Consulting
>> * w w w .pearce.uk . com
>
>
>Hey Don,
>
>Here's how I see this. In your first case, the 41.1K and 47.1 K components are sidebands of
>the 44.1K carrier. In the second case those same components are the (folded) sidebands (or
>negative-frequency, which is perfectly valid)) of a 3 KHz carrier. The result is the
>same -- they're the same sum and difference frequencies -- they don't really care who's
>modulating whom! :) A sum frequency is a sum, and a difference is a difference. The only
>real difference is if you add 0 Hz (DC offset) to either the audio or to the carrier. In
>the case of the former, you get the 44.1K carrier component as well as the sidebands around
>it, and in the latter you get baseband audio as well as the same sidebands around 44.1K.
>And that's the result of the sum and difference frequencies too. Ain't no getting away from
>it!
>
Yes - that is how I see it.
>You mentioned generating suppressed-carrier generation, by filtering out the 3K component.
>I think you can just multiply the signal with the baseband, adding 0 Hz (DC) to neither, and
>get that. You have to use a four-quadrant multiplier (handles both negative and positive
>signals). You should get no carrier and no baseband in the output -- just the sidebands.
>ATSC TV adds a little DC to get a little bit of carrier (if I understand it correctly, and
>I'm not at all sure I do) for recovery. At least that's one way of implementing it.
>
Right - I've done this with a double balanced mixer and a bit of
adjustable DC bias to null the carrier completely (more or less).
>Forgive my excess of clarification comments in all this -- I don't mean to be pedantic, but
>I try to be as clear as possible, and I think they might be useful to some of those who
>might be following this thread.
>
No, that's fine. This can all get very complicated unless you have
some simple way of visualising it.
>The terms "mirror" and "image," I think, at least as used in superhet radio, refer to such
>things as a modulation product that is the sum frequency, where only the difference was
>wanted. It's a mirror around the local oscillator frequency. But in a more general sense,
>any modulation product that winds up in your frequency band of interest (audio, in our case)
>is an ambiguous component, in that we can't distinguish it from a real signal component.
>I've always thought of any as an alias.
>
An alias is a specific kind of image with a specific set of
properties. It can only occur as a result of discrete-time sampling.
All the stuff that comes of a normal modulator is an image - or an
intermod product if we have any non-linearity.
>Here's my main thrust: I think the aliases we get in sampled audio where the audio goes
>above Nyquist are simply the difference modulation products, which creep into our baseband
>if the audio goes above Nyquist. As the audio gets higher in frequency, the sidebands get
>lower, from 44.1K. Nyquist is simply the midpoint, where they meet. Sampling is a case of
>general modulation theory.
>
>Hoping to hear your comments.
Well, since sampling is a form of modulation, I have to agree. But as
I say it is a form of modulation product that can only exist in a
sampled system, so I think it is fair to treat it as a special case.
Also it is occurring in a situation we would not usually think of as
modulation (even though it is). Anywhere two signals are multiplied
(an ADC multiplies the audio by the sampling pulse) there will be
modulation products.
d
--
Pearce Consulting
* w w w .pearce.uk . com
On Thu, 15 May 2008 21:38:09 GMT, "Earl Kiosterud"
<someone@nowhere . com > wrote:
>
>
>"Don Pearce" <nospam@nospam . com > wrote in message news:482e5bea.25475953@news.plus . net ...
>(snip)
>>
>> Let me think about this! I'll do the maths later. I think you are
>> right that you will get stuff all over the place that you don't want,
>> but I think I would tend to call them images rather than aliases.
>>
>> I also suspect that the use of a synchronous demodulator might let you
>> recover the signals (as you can recover modulation over 100% this
>> way), meaning that the signals aren't truly jumbled - they just appear
>> that way. Aliasing is truly there for ever once it happens - there is
>> no way back.
>>
>> OK, let me change my mind. I've just used Mathcad to look at this. I
>> made two FFT spectra - one with 44.1k as the carrier and 3k as the
>> modulation and the other with 3k as the carrier and 44.1k as the
>> modulation.
>>
>> For the first I see a carrier at 44.1kHz, and sidebands at 41.1 and
>> 47.1kHz. Exactly as you expect.
>>
>> For the second I see a carrier at 3kHz and sidebands at 44.1 and
>> 47.1kHz. Which is exactly as you expect once you know what to expect
>> ;-)
>>
>> Which will do for me. It would even be a nice way to generate
>> suppressed carrier AM - just filter away the 3kHz when done
>> modulating.
>>
>> d
>>
>>
>> --
>> Pearce Consulting
>> * w w w .pearce.uk . com
>
>
>Hey Don,
>
>Here's how I see this. In your first case, the 41.1K and 47.1 K components are sidebands of
>the 44.1K carrier. In the second case those same components are the (folded) sidebands (or
>negative-frequency, which is perfectly valid)) of a 3 KHz carrier. The result is the
>same -- they're the same sum and difference frequencies -- they don't really care who's
>modulating whom! :) A sum frequency is a sum, and a difference is a difference. The only
>real difference is if you add 0 Hz (DC offset) to either the audio or to the carrier. In
>the case of the former, you get the 44.1K carrier component as well as the sidebands around
>it, and in the latter you get baseband audio as well as the same sidebands around 44.1K.
>And that's the result of the sum and difference frequencies too. Ain't no getting away from
>it!
>
Yes - that is how I see it.
>You mentioned generating suppressed-carrier generation, by filtering out the 3K component.
>I think you can just multiply the signal with the baseband, adding 0 Hz (DC) to neither, and
>get that. You have to use a four-quadrant multiplier (handles both negative and positive
>signals). You should get no carrier and no baseband in the output -- just the sidebands.
>ATSC TV adds a little DC to get a little bit of carrier (if I understand it correctly, and
>I'm not at all sure I do) for recovery. At least that's one way of implementing it.
>
Right - I've done this with a double balanced mixer and a bit of
adjustable DC bias to null the carrier completely (more or less).
>Forgive my excess of clarification comments in all this -- I don't mean to be pedantic, but
>I try to be as clear as possible, and I think they might be useful to some of those who
>might be following this thread.
>
No, that's fine. This can all get very complicated unless you have
some simple way of visualising it.
>The terms "mirror" and "image," I think, at least as used in superhet radio, refer to such
>things as a modulation product that is the sum frequency, where only the difference was
>wanted. It's a mirror around the local oscillator frequency. But in a more general sense,
>any modulation product that winds up in your frequency band of interest (audio, in our case)
>is an ambiguous component, in that we can't distinguish it from a real signal component.
>I've always thought of any as an alias.
>
An alias is a specific kind of image with a specific set of
properties. It can only occur as a result of discrete-time sampling.
All the stuff that comes of a normal modulator is an image - or an
intermod product if we have any non-linearity.
>Here's my main thrust: I think the aliases we get in sampled audio where the audio goes
>above Nyquist are simply the difference modulation products, which creep into our baseband
>if the audio goes above Nyquist. As the audio gets higher in frequency, the sidebands get
>lower, from 44.1K. Nyquist is simply the midpoint, where they meet. Sampling is a case of
>general modulation theory.
>
>Hoping to hear your comments.
Well, since sampling is a form of modulation, I have to agree. But as
I say it is a form of modulation product that can only exist in a
sampled system, so I think it is fair to treat it as a special case.
Also it is occurring in a situation we would not usually think of as
modulation (even though it is). Anywhere two signals are multiplied
(an ADC multiplies the audio by the sampling pulse) there will be
modulation products.
d
--
Pearce Consulting
* w w w .pearce.uk . com
Re: Are purely-analog audio devices immune to aliasing?
"Don Pearce" <nospam@nospam . com > wrote in message news:482caf60.46834968@news.plus . net ...
(snip)
>>
>>Hey Don,
>>
>>Here's how I see this. In your first case, the 41.1K and 47.1 K components are sidebands
>>of
>>the 44.1K carrier. In the second case those same components are the (folded) sidebands
>>(or
>>negative-frequency, which is perfectly valid)) of a 3 KHz carrier. The result is the
>>same -- they're the same sum and difference frequencies -- they don't really care who's
>>modulating whom! :) A sum frequency is a sum, and a difference is a difference. The only
>>real difference is if you add 0 Hz (DC offset) to either the audio or to the carrier. In
>>the case of the former, you get the 44.1K carrier component as well as the sidebands
>>around
>>it, and in the latter you get baseband audio as well as the same sidebands around 44.1K.
>>And that's the result of the sum and difference frequencies too. Ain't no getting away
>>from
>>it!
>>
> Yes - that is how I see it.
>
>>You mentioned generating suppressed-carrier generation, by filtering out the 3K component.
>>I think you can just multiply the signal with the baseband, adding 0 Hz (DC) to neither,
>>and
>>get that. You have to use a four-quadrant multiplier (handles both negative and positive
>>signals). You should get no carrier and no baseband in the output -- just the sidebands.
>>ATSC TV adds a little DC to get a little bit of carrier (if I understand it correctly, and
>>I'm not at all sure I do) for recovery. At least that's one way of implementing it.
>>
> Right - I've done this with a double balanced mixer and a bit of
> adjustable DC bias to null the carrier completely (more or less).
>
>>Forgive my excess of clarification comments in all this -- I don't mean to be pedantic,
>>but
>>I try to be as clear as possible, and I think they might be useful to some of those who
>>might be following this thread.
>>
>
> No, that's fine. This can all get very complicated unless you have
> some simple way of visualising it.
>
>>The terms "mirror" and "image," I think, at least as used in superhet radio, refer to such
>>things as a modulation product that is the sum frequency, where only the difference was
>>wanted. It's a mirror around the local oscillator frequency. But in a more general
>>sense,
>>any modulation product that winds up in your frequency band of interest (audio, in our
>>case)
>>is an ambiguous component, in that we can't distinguish it from a real signal component.
>>I've always thought of any as an alias.
>>
> An alias is a specific kind of image with a specific set of
> properties. It can only occur as a result of discrete-time sampling.
> All the stuff that comes of a normal modulator is an image - or an
> intermod product if we have any non-linearity.
>
>>Here's my main thrust: I think the aliases we get in sampled audio where the audio goes
>>above Nyquist are simply the difference modulation products, which creep into our baseband
>>if the audio goes above Nyquist. As the audio gets higher in frequency, the sidebands get
>>lower, from 44.1K. Nyquist is simply the midpoint, where they meet. Sampling is a case
>>of
>>general modulation theory.
>>
>>Hoping to hear your comments.
>
> Well, since sampling is a form of modulation, I have to agree. But as
> I say it is a form of modulation product that can only exist in a
> sampled system, so I think it is fair to treat it as a special case.
> Also it is occurring in a situation we would not usually think of as
> modulation (even though it is). Anywhere two signals are multiplied
> (an ADC multiplies the audio by the sampling pulse) there will be
> modulation products.
>
> d
> --
> Pearce Consulting
> * w w w .pearce.uk . com
Don
The reason I posed my little AM modulator, using a multiplier with some 0 Hz added to the
44.1K carrier was to show that it's exactly the same in this continuous (non-sampled) system
as the aliasing in CD audio. The result is exactly the same in either system, and my point
is that it's for the same reasons. It's all about modulation products. I don't understand
why you say it can happen only in a sampling system. Could you elaborate?
Do you agree that the output of the DAC will contain the baseband components, and a set of
sidebands around 44.1K patterned like the baseband? (Also around 88.2K, etc.)
--
Regards from soon-to-be-raining -- again -- Virginia Beach,
Earl
"Don Pearce" <nospam@nospam . com > wrote in message news:482caf60.46834968@news.plus . net ...
(snip)
>>
>>Hey Don,
>>
>>Here's how I see this. In your first case, the 41.1K and 47.1 K components are sidebands
>>of
>>the 44.1K carrier. In the second case those same components are the (folded) sidebands
>>(or
>>negative-frequency, which is perfectly valid)) of a 3 KHz carrier. The result is the
>>same -- they're the same sum and difference frequencies -- they don't really care who's
>>modulating whom! :) A sum frequency is a sum, and a difference is a difference. The only
>>real difference is if you add 0 Hz (DC offset) to either the audio or to the carrier. In
>>the case of the former, you get the 44.1K carrier component as well as the sidebands
>>around
>>it, and in the latter you get baseband audio as well as the same sidebands around 44.1K.
>>And that's the result of the sum and difference frequencies too. Ain't no getting away
>>from
>>it!
>>
> Yes - that is how I see it.
>
>>You mentioned generating suppressed-carrier generation, by filtering out the 3K component.
>>I think you can just multiply the signal with the baseband, adding 0 Hz (DC) to neither,
>>and
>>get that. You have to use a four-quadrant multiplier (handles both negative and positive
>>signals). You should get no carrier and no baseband in the output -- just the sidebands.
>>ATSC TV adds a little DC to get a little bit of carrier (if I understand it correctly, and
>>I'm not at all sure I do) for recovery. At least that's one way of implementing it.
>>
> Right - I've done this with a double balanced mixer and a bit of
> adjustable DC bias to null the carrier completely (more or less).
>
>>Forgive my excess of clarification comments in all this -- I don't mean to be pedantic,
>>but
>>I try to be as clear as possible, and I think they might be useful to some of those who
>>might be following this thread.
>>
>
> No, that's fine. This can all get very complicated unless you have
> some simple way of visualising it.
>
>>The terms "mirror" and "image," I think, at least as used in superhet radio, refer to such
>>things as a modulation product that is the sum frequency, where only the difference was
>>wanted. It's a mirror around the local oscillator frequency. But in a more general
>>sense,
>>any modulation product that winds up in your frequency band of interest (audio, in our
>>case)
>>is an ambiguous component, in that we can't distinguish it from a real signal component.
>>I've always thought of any as an alias.
>>
> An alias is a specific kind of image with a specific set of
> properties. It can only occur as a result of discrete-time sampling.
> All the stuff that comes of a normal modulator is an image - or an
> intermod product if we have any non-linearity.
>
>>Here's my main thrust: I think the aliases we get in sampled audio where the audio goes
>>above Nyquist are simply the difference modulation products, which creep into our baseband
>>if the audio goes above Nyquist. As the audio gets higher in frequency, the sidebands get
>>lower, from 44.1K. Nyquist is simply the midpoint, where they meet. Sampling is a case
>>of
>>general modulation theory.
>>
>>Hoping to hear your comments.
>
> Well, since sampling is a form of modulation, I have to agree. But as
> I say it is a form of modulation product that can only exist in a
> sampled system, so I think it is fair to treat it as a special case.
> Also it is occurring in a situation we would not usually think of as
> modulation (even though it is). Anywhere two signals are multiplied
> (an ADC multiplies the audio by the sampling pulse) there will be
> modulation products.
>
> d
> --
> Pearce Consulting
> * w w w .pearce.uk . com
Don
The reason I posed my little AM modulator, using a multiplier with some 0 Hz added to the
44.1K carrier was to show that it's exactly the same in this continuous (non-sampled) system
as the aliasing in CD audio. The result is exactly the same in either system, and my point
is that it's for the same reasons. It's all about modulation products. I don't understand
why you say it can happen only in a sampling system. Could you elaborate?
Do you agree that the output of the DAC will contain the baseband components, and a set of
sidebands around 44.1K patterned like the baseband? (Also around 88.2K, etc.)
--
Regards from soon-to-be-raining -- again -- Virginia Beach,
Earl
Re: Are purely-analog audio devices immune to aliasing?
Earl Kiosterud wrote:
> "Don Pearce" <nospam@nospam . com > wrote in message news:482caf60.46834968@news.plus . net ...
> (snip)
>>> Hey Don,
>>>
>>> Here's how I see this. In your first case, the 41.1K and 47.1 K components are sidebands
>>> of
>>> the 44.1K carrier. In the second case those same components are the (folded) sidebands
>>> (or
>>> negative-frequency, which is perfectly valid)) of a 3 KHz carrier. The result is the
>>> same -- they're the same sum and difference frequencies -- they don't really care who's
>>> modulating whom! :) A sum frequency is a sum, and a difference is a difference. The only
>>> real difference is if you add 0 Hz (DC offset) to either the audio or to the carrier. In
>>> the case of the former, you get the 44.1K carrier component as well as the sidebands
>>> around
>>> it, and in the latter you get baseband audio as well as the same sidebands around 44.1K.
>>> And that's the result of the sum and difference frequencies too. Ain't no getting away
>>> from
>>> it!
>>>
>> Yes - that is how I see it.
>>
>>> You mentioned generating suppressed-carrier generation, by filtering out the 3K component.
>>> I think you can just multiply the signal with the baseband, adding 0 Hz (DC) to neither,
>>> and
>>> get that. You have to use a four-quadrant multiplier (handles both negative and positive
>>> signals). You should get no carrier and no baseband in the output -- just the sidebands.
>>> ATSC TV adds a little DC to get a little bit of carrier (if I understand it correctly, and
>>> I'm not at all sure I do) for recovery. At least that's one way of implementing it.
>>>
>> Right - I've done this with a double balanced mixer and a bit of
>> adjustable DC bias to null the carrier completely (more or less).
>>
>>> Forgive my excess of clarification comments in all this -- I don't mean to be pedantic,
>>> but
>>> I try to be as clear as possible, and I think they might be useful to some of those who
>>> might be following this thread.
>>>
>> No, that's fine. This can all get very complicated unless you have
>> some simple way of visualising it.
>>
>>> The terms "mirror" and "image," I think, at least as used in superhet radio, refer to such
>>> things as a modulation product that is the sum frequency, where only the difference was
>>> wanted. It's a mirror around the local oscillator frequency. But in a more general
>>> sense,
>>> any modulation product that winds up in your frequency band of interest (audio, in our
>>> case)
>>> is an ambiguous component, in that we can't distinguish it from a real signal component.
>>> I've always thought of any as an alias.
>>>
>> An alias is a specific kind of image with a specific set of
>> properties. It can only occur as a result of discrete-time sampling.
>> All the stuff that comes of a normal modulator is an image - or an
>> intermod product if we have any non-linearity.
>>
>>> Here's my main thrust: I think the aliases we get in sampled audio where the audio goes
>>> above Nyquist are simply the difference modulation products, which creep into our baseband
>>> if the audio goes above Nyquist. As the audio gets higher in frequency, the sidebands get
>>> lower, from 44.1K. Nyquist is simply the midpoint, where they meet. Sampling is a case
>>> of
>>> general modulation theory.
>>>
>>> Hoping to hear your comments.
>> Well, since sampling is a form of modulation, I have to agree. But as
>> I say it is a form of modulation product that can only exist in a
>> sampled system, so I think it is fair to treat it as a special case.
>> Also it is occurring in a situation we would not usually think of as
>> modulation (even though it is). Anywhere two signals are multiplied
>> (an ADC multiplies the audio by the sampling pulse) there will be
>> modulation products.
>>
>> d
>> --
>> Pearce Consulting
>> * w w w .pearce.uk . com
>
> Don
>
> The reason I posed my little AM modulator, using a multiplier with some 0 Hz added to the
> 44.1K carrier was to show that it's exactly the same in this continuous (non-sampled) system
> as the aliasing in CD audio. The result is exactly the same in either system, and my point
> is that it's for the same reasons. It's all about modulation products. I don't understand
> why you say it can happen only in a sampling system. Could you elaborate?
>
> Do you agree that the output of the DAC will contain the baseband components, and a set of
> sidebands around 44.1K patterned like the baseband? (Also around 88.2K, etc.)
Yes, I can see this is a matter of how you view things.
An ADC is like an AM modulator (OK it is an AM modulator) and it
produces image sidebands in exactly the way any of them does. The big
difference with most modulation systems is that in an ADC, the carrier
(44.1kHz) isn't symmetric - it is entirely one sided. For that reason
baseband comes through it and in this case it becomes our wanted signal.
Of course this will happen whether the modulator is sampled, as in an
ADC or continuous. The rest of the alias productsaround 88.2kHz etc can
only happen in a sampling system, and are true aliases.
d
Earl Kiosterud wrote:
> "Don Pearce" <nospam@nospam . com > wrote in message news:482caf60.46834968@news.plus . net ...
> (snip)
>>> Hey Don,
>>>
>>> Here's how I see this. In your first case, the 41.1K and 47.1 K components are sidebands
>>> of
>>> the 44.1K carrier. In the second case those same components are the (folded) sidebands
>>> (or
>>> negative-frequency, which is perfectly valid)) of a 3 KHz carrier. The result is the
>>> same -- they're the same sum and difference frequencies -- they don't really care who's
>>> modulating whom! :) A sum frequency is a sum, and a difference is a difference. The only
>>> real difference is if you add 0 Hz (DC offset) to either the audio or to the carrier. In
>>> the case of the former, you get the 44.1K carrier component as well as the sidebands
>>> around
>>> it, and in the latter you get baseband audio as well as the same sidebands around 44.1K.
>>> And that's the result of the sum and difference frequencies too. Ain't no getting away
>>> from
>>> it!
>>>
>> Yes - that is how I see it.
>>
>>> You mentioned generating suppressed-carrier generation, by filtering out the 3K component.
>>> I think you can just multiply the signal with the baseband, adding 0 Hz (DC) to neither,
>>> and
>>> get that. You have to use a four-quadrant multiplier (handles both negative and positive
>>> signals). You should get no carrier and no baseband in the output -- just the sidebands.
>>> ATSC TV adds a little DC to get a little bit of carrier (if I understand it correctly, and
>>> I'm not at all sure I do) for recovery. At least that's one way of implementing it.
>>>
>> Right - I've done this with a double balanced mixer and a bit of
>> adjustable DC bias to null the carrier completely (more or less).
>>
>>> Forgive my excess of clarification comments in all this -- I don't mean to be pedantic,
>>> but
>>> I try to be as clear as possible, and I think they might be useful to some of those who
>>> might be following this thread.
>>>
>> No, that's fine. This can all get very complicated unless you have
>> some simple way of visualising it.
>>
>>> The terms "mirror" and "image," I think, at least as used in superhet radio, refer to such
>>> things as a modulation product that is the sum frequency, where only the difference was
>>> wanted. It's a mirror around the local oscillator frequency. But in a more general
>>> sense,
>>> any modulation product that winds up in your frequency band of interest (audio, in our
>>> case)
>>> is an ambiguous component, in that we can't distinguish it from a real signal component.
>>> I've always thought of any as an alias.
>>>
>> An alias is a specific kind of image with a specific set of
>> properties. It can only occur as a result of discrete-time sampling.
>> All the stuff that comes of a normal modulator is an image - or an
>> intermod product if we have any non-linearity.
>>
>>> Here's my main thrust: I think the aliases we get in sampled audio where the audio goes
>>> above Nyquist are simply the difference modulation products, which creep into our baseband
>>> if the audio goes above Nyquist. As the audio gets higher in frequency, the sidebands get
>>> lower, from 44.1K. Nyquist is simply the midpoint, where they meet. Sampling is a case
>>> of
>>> general modulation theory.
>>>
>>> Hoping to hear your comments.
>> Well, since sampling is a form of modulation, I have to agree. But as
>> I say it is a form of modulation product that can only exist in a
>> sampled system, so I think it is fair to treat it as a special case.
>> Also it is occurring in a situation we would not usually think of as
>> modulation (even though it is). Anywhere two signals are multiplied
>> (an ADC multiplies the audio by the sampling pulse) there will be
>> modulation products.
>>
>> d
>> --
>> Pearce Consulting
>> * w w w .pearce.uk . com
>
> Don
>
> The reason I posed my little AM modulator, using a multiplier with some 0 Hz added to the
> 44.1K carrier was to show that it's exactly the same in this continuous (non-sampled) system
> as the aliasing in CD audio. The result is exactly the same in either system, and my point
> is that it's for the same reasons. It's all about modulation products. I don't understand
> why you say it can happen only in a sampling system. Could you elaborate?
>
> Do you agree that the output of the DAC will contain the baseband components, and a set of
> sidebands around 44.1K patterned like the baseband? (Also around 88.2K, etc.)
Yes, I can see this is a matter of how you view things.
An ADC is like an AM modulator (OK it is an AM modulator) and it
produces image sidebands in exactly the way any of them does. The big
difference with most modulation systems is that in an ADC, the carrier
(44.1kHz) isn't symmetric - it is entirely one sided. For that reason
baseband comes through it and in this case it becomes our wanted signal.
Of course this will happen whether the modulator is sampled, as in an
ADC or continuous. The rest of the alias productsaround 88.2kHz etc can
only happen in a sampling system, and are true aliases.
d
Re: Are purely-analog audio devices immune to aliasing?
Don Pearce wrote:
> Let me think about this! I'll do the maths later. I think you are
> right that you will get stuff all over the place that you don't want,
> but I think I would tend to call them images rather than aliases.
That was the analogy I was drawing with my "LSB/USB" post. That the sum and
difference frequencies are in som way analogous to the frequency products
from aliasing.
geoff
Don Pearce wrote:
> Let me think about this! I'll do the maths later. I think you are
> right that you will get stuff all over the place that you don't want,
> but I think I would tend to call them images rather than aliases.
That was the analogy I was drawing with my "LSB/USB" post. That the sum and
difference frequencies are in som way analogous to the frequency products
from aliasing.
geoff
Re: Are purely-analog audio devices immune to aliasing?
geoff wrote:
> Don Pearce wrote:
>> Let me think about this! I'll do the maths later. I think you are
>> right that you will get stuff all over the place that you don't want,
>> but I think I would tend to call them images rather than aliases.
>
> That was the analogy I was drawing with my "LSB/USB" post. That the sum and
> difference frequencies are in som way analogous to the frequency products
> from aliasing.
>
> geoff
>
>
Yes they are analogous in that a sampling device will also produce them.
The difference is that the sampler also produces a comb of them up to
infinity. You could say that the analogue image products are the limit
case of aliasing when the dead space approaches zero.
d
geoff wrote:
> Don Pearce wrote:
>> Let me think about this! I'll do the maths later. I think you are
>> right that you will get stuff all over the place that you don't want,
>> but I think I would tend to call them images rather than aliases.
>
> That was the analogy I was drawing with my "LSB/USB" post. That the sum and
> difference frequencies are in som way analogous to the frequency products
> from aliasing.
>
> geoff
>
>
Yes they are analogous in that a sampling device will also produce them.
The difference is that the sampler also produces a comb of them up to
infinity. You could say that the analogue image products are the limit
case of aliasing when the dead space approaches zero.
d
Re: Are purely-analog audio devices immune to aliasing?
On May 15, 6:04 pm, Don Pearce <nos...@nospam . com > wrote:
> geoff wrote:
> > Don Pearce wrote:
> >> Let me think about this! I'll do the maths later. I think you are
> >> right that you will get stuff all over the place that you don't want,
> >> but I think I would tend to call them images rather than aliases.
>
> > That was the analogy I was drawing with my "LSB/USB" post. That the sum and
> > difference frequencies are in som way analogous to the frequency products
> > from aliasing.
>
> > geoff
>
> Yes they are analogous in that a sampling device will also produce them.
> The difference is that the sampler also produces a comb of them up to
> infinity. You could say that the analogue image products are the limit
> case of aliasing when the dead space approaches zero.
>
> d
On May 15, 6:04 pm, Don Pearce <nos...@nospam . com > wrote:
> geoff wrote:
> > Don Pearce wrote:
> >> Let me think about this! I'll do the maths later. I think you are
> >> right that you will get stuff all over the place that you don't want,
> >> but I think I would tend to call them images rather than aliases.
>
> > That was the analogy I was drawing with my "LSB/USB" post. That the sum and
> > difference frequencies are in som way analogous to the frequency products
> > from aliasing.
>
> > geoff
>
> Yes they are analogous in that a sampling device will also produce them.
> The difference is that the sampler also produces a comb of them up to
> infinity. You could say that the analogue image products are the limit
> case of aliasing when the dead space approaches zero.
>
> d
Re: Are purely-analog audio devices immune to aliasing?
On May 15, 6:04 pm, Don Pearce <nos...@nospam . com > wrote:
> geoff wrote:
> > Don Pearce wrote:
> >> Let me think about this! I'll do the maths later. I think you are
> >> right that you will get stuff all over the place that you don't want,
> >> but I think I would tend to call them images rather than aliases.
>
> > That was the analogy I was drawing with my "LSB/USB" post. That the sum and
> > difference frequencies are in som way analogous to the frequency products
> > from aliasing.
>
> > geoff
>
> Yes they are analogous in that a sampling device will also produce them.
> The difference is that the sampler also produces a comb of them up to
> infinity. You could say that the analogue image products are the limit
> case of aliasing when the dead space approaches zero.
The reason is very simple. IN the case of AM modulation,
the carrier is a sine wave, which has but a single component,
the fundamental of the carrier.
When "sampling," in the context you're using it, the
"carrier is actually a train of narrow pulses. Look at
it's specturm: it's a series of components evenly
space out to infinity (assuming 0 rise and fall time),
so you have the images spread out to infinity as
well.
Remember that what we are talking about "sampling"
is often also referred to as "pulse code modulation,"
or PCM.
It's exactly the same (save that the generated "sidebands
are reallu "images," not "aliases"
The reason you have aliases with "sampling (or modulating
a pulse train) is because of all those other components:
something far out of band will also generate an infinite
number of images, which can fall back or "alias" into
your basebnand and thus be indistiguishable from a
true base-band signal.
Can it happen in an all-anolg system? Sure, just come up
with a carrier that's a sufficiently comples waveform.
Condiser, for example, your carrier having TWO components:
a sine at 44.1 kHz and one at 88.2 kHz. Now, modulate that
with a signal at. oh 88.2+-43 kHz, Where do the sidebands
end up?!
On May 15, 6:04 pm, Don Pearce <nos...@nospam . com > wrote:
> geoff wrote:
> > Don Pearce wrote:
> >> Let me think about this! I'll do the maths later. I think you are
> >> right that you will get stuff all over the place that you don't want,
> >> but I think I would tend to call them images rather than aliases.
>
> > That was the analogy I was drawing with my "LSB/USB" post. That the sum and
> > difference frequencies are in som way analogous to the frequency products
> > from aliasing.
>
> > geoff
>
> Yes they are analogous in that a sampling device will also produce them.
> The difference is that the sampler also produces a comb of them up to
> infinity. You could say that the analogue image products are the limit
> case of aliasing when the dead space approaches zero.
The reason is very simple. IN the case of AM modulation,
the carrier is a sine wave, which has but a single component,
the fundamental of the carrier.
When "sampling," in the context you're using it, the
"carrier is actually a train of narrow pulses. Look at
it's specturm: it's a series of components evenly
space out to infinity (assuming 0 rise and fall time),
so you have the images spread out to infinity as
well.
Remember that what we are talking about "sampling"
is often also referred to as "pulse code modulation,"
or PCM.
It's exactly the same (save that the generated "sidebands
are reallu "images," not "aliases"
The reason you have aliases with "sampling (or modulating
a pulse train) is because of all those other components:
something far out of band will also generate an infinite
number of images, which can fall back or "alias" into
your basebnand and thus be indistiguishable from a
true base-band signal.
Can it happen in an all-anolg system? Sure, just come up
with a carrier that's a sufficiently comples waveform.
Condiser, for example, your carrier having TWO components:
a sine at 44.1 kHz and one at 88.2 kHz. Now, modulate that
with a signal at. oh 88.2+-43 kHz, Where do the sidebands
end up?!
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