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



"Don Pearce" <nospam@xxxxxxxxxx> wrote in message news:482e5bea.25475953@xxxxxxxxxxxxxxxx
(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
http://www.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


.

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