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Re: Well, the "how' is not hard to understand.

"Don't forget a song of any length can be decomposed into a (rather large, complex) Fourier Series...
"

Oh I am aware of it, JJ. As part of my work, we use the Fourier Transform to convert time based measurements into frequency based results. What I find interesting are transients, such as a rimshot, which come and go rather quickly (in the audio sense anyway). Now since this is a non-repeating signal when one performs a fourier transform you will see a lot of frequency components that are related to the peak width, rise time, and decay of that transient.

An example from science. We have mass spectral peaks that are on the order of a few nano-seconds wide. We were having problems with ringing to due to impedance mismatches in our detection system. We did a spectrum analysis of this peak to find out over what range the frequencies in this transient are spread and it turned out that they were spread over several hundred MHz. So the impedance of our system had to be corrected over this bandwidth. So clearly, a fourier series can transform a transient into its component sine waves but it is often a very complex mix of waves over a very wide bandwidth that is almost certainly extending well above 20Khz (Boyk has shown that cymbals in particular have a lot of content above 20Khz).

The question then is how well do the theories behind sampling deal with this in terms of practical digital filters? Does it also have consequences for data converted below Nyquist? Have you compared a live transient response fed directly into a spectrum analyzer (a high resolution one that is) and then done the same thing with a digital recording of the same live event played back through a DAC into the same spectrum analyzer? If not this could be interesting. If so, what was the result? Obviously, all ultra-sonic information will be heavily rolled off (if its 16/44 that is) compared to the live feed but what about the frequencies below Nyquist? Are they one to one the same frequencies and with the same amplitudes? If not then it could result in a change in the "color" of instruments.

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  • Re: Well, the "how' is not hard to understand. - morricab 06/23/0606:04:01 06/23/06 (1)
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