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Re: Loopers-Delight-d Digest V05 #834
Yes, fourier falls apart (even in theory) when applied to non-stationary signals. I agree with that.
Maybe we're comparing apples and oranges here - I'm claiming that the
Nyquist theorem is a mathematical proof that you can perfectly
reconstruct a stationary, periodic signal given perfect components to
>>Unless my math is wrong, I don't agree. A 22khz tone sampled at
>>44.1khz produces a signal containing the fundamental (22k) plus
>>additional components at 22.1k, 66.1k, 66.2k, 110.2k, 110.3k,
>>154.3k, ad infinitum. Do you agree?
>for one thing this ignores aliasing.
What are the alias frequencies in this example? I'm not seeing them.
I don't see how the two sampled signals you described are mathematically equivalent.
On 12/21/05, a k butler <firstname.lastname@example.org> wrote:
At 22:24 21/12/05, you wrote:
> > sample a 22kHz signal at 44.1kHz
> > the result is identical to sampling a 22.05kHz tone
> > which is amplitude modulated at 500Hz
> > agree? (if no, then try working it out on paper)
just draw the waveform,
and put the sample points on
then you'll see it
for being unclear, I didn't mean to do the arithmetic
>Unless my math is wrong, I don't agree. A 22khz tone sampled at
>44.1khz produces a signal containing the fundamental (22k) plus
>additional components at 22.1k, 66.1k, 66.2k, 110.2k, 110.3k,
>154.3k, ad infinitum. Do you agree?
for one thing this ignores aliasing.
secondly, only 22.1k is within the limits imposed by the sampling frequency.
thirdly, ;-) it's getting late here and I'm a bit tired to crunch the numbers,
I will do later, but once you see the samples plotted the maths won't matter
>I may be misinterpreting "the result is identical to sampling a 22.05kHz tone
>which is amplitude modulated at 500Hz". I'm assuming you're first
>modulating a 22.05k tone at 500hz, producing the original
>tone plus sidebands at 22.55k and 21.55k. Sample that signal and
>you don't get the same result as the 22k tone sampled at 44.1k.
>Which is wrong? My math, my interpretation, or both?
>The ideal Nyquist sampling theorem is based on the ideal Fourier
>transform - ideal Fourier transforms are lossless aren't
>they? Granted it all falls apart when you try to put it into practice.
um, I already dealt with that.
Ideal fourier presumes a periodic signal of known frequency.
So it falls apart in theory, even before the practice