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In Reply to: RE: Question about DSP and Filtering posted by John Swenson on July 20, 2012 at 15:54:49:
"In this forum there have been a lot of statements along the lines of "Shannon says that the filter will accurately reproduce the original waveform", but many are saying it doesn't sound that way, and others keep on saying the theorum is correct, I think this is reason for the dichotomy, the actual hardware implementations in most cases are NOT properly implementing the filter."
Shannon's theorem is just theory, i.e. it works "perfectly" in a perfect world. In an imperfect world, it works imperfectly. The basic assumption used in the theory is that the input signal to be reconstructed is band limited and contains nothing at or above FS/2. Not only is this assumption inapplicable for all audio files, it is impossible, and that for two separate reasons:
(1) Except for the all zero signal there can be no finite bandwidth signal of finite duration. This rules out all finite duration musical files. (Ironically, in his classic paper, Shannon made a mistake, presumably a typo in his Theorem 1, when he failed to rule out energy at the Nyquist frequency.)
(2) The theorem is based on real numbers. Computers are finite state machines and can not do accurate processing on real numbers.
This means that the result of filtering will not be the original signal, but merely some kind of approximation to it. We are left hoping that the approximation sounds the same, but this outcome can not be guaranteed by relying on theory.
Tony Lauck
"Diversity is the law of nature; no two entities in this universe are uniform." - P.R. Sarkar
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Follow Ups
- Theory vs. Practice - Tony Lauck 08:19:04 07/21/12 (1)
- Nyquist Shannon - play-mate 22:36:52 09/02/12 (0)
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