Earl Kiosterud wrote:
> "Don Pearce" <nospam@[EMAIL PROTECTED]
> wrote in message
news:482caf60.46834968@[EMAIL PROTECTED]
> (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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