Re: Are purely-analog audio devices immune to aliasing?

Earl Kiosterud wrote:
"Don Pearce" <nospam@xxxxxxxxxx> wrote in message news:482caf60.46834968@xxxxxxxxxxxxxxxx
(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
http://www.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
.

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