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**To**:**Loopers-Delight@loopers-delight.com****From**:**Tom Combs <tncombs@gmail.com>****Subject**:**Re: Loopers-Delight-d Digest V05 #834****Date**:**Wed, 21 Dec 2005 21:41:42 -0500**

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 work with.

>>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?

>no,

>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** <akbutler@tiscali.co.uk> 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

...easy

then you'll see it

sorry

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?

no,

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 22.05k

>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

andy

**References**:- Re: Loopers-Delight-d Digest V05 #834
*From:*a k butler <akbutler@tiscali.co.uk>

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