Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site petrus.UUCP Path: utzoo!watmath!clyde!burl!ulysses!allegra!bellcore!petrus!karn From: karn@petrus.UUCP Newsgroups: net.audio Subject: Re: CD Reflections - 44.1k? Message-ID: <258@petrus.UUCP> Date: Wed, 16-Jan-85 12:22:41 EST Article-I.D.: petrus.258 Posted: Wed Jan 16 12:22:41 1985 Date-Received: Thu, 17-Jan-85 13:57:03 EST References: <15100001@hpfcmp.UUCP> <3411@mit-eddie.UUCP> <1420@hplabs.UUCP> <755@clyde.UUCP> Organization: Bell Communications Research, Inc Lines: 39 > Now for the part that bothers me: The Nyquist theorem always seems to > be based on continuous signals. I.e, the reason you can sample a 20k > signal at just slightly more than 40k is that EVENTUALLY you will get > some samples around the peak amplitude - you will also get some around > zero. But music isn't like that - notes start and end. In effect, you > are multiplying (or modulating) the sine wave by an envelope which also > contributes to the spectrum. HOW MUCH ADDED SAMPLING DOES THIS REQUIRE? > I don't want to listen to a 20k sine wave, I want transients (anybody > remember TIM distortion?). How about it digital types? - any guesses? > The Nyquist theorem is valid for ANY bandlimited signal, it doesn't matter whether it is periodic or not. One way to visualize this intuitively is that any signal which has been bandlimited (whether it be a transient or a periodic waveform) is limited in how fast the signal voltage can change with respect to time. This places a bound on how fast the signal must be sampled in order to capture *all* of the information within it. If the transient contains high frequency signals which cannot be sampled fast enough, they must be removed by the pre-sampling low pass filter or else aliasing distortion will result. But as long as the sampling rate is at least twice as fast as the cutoff of the low pass filter, then the sampling operation will retain ALL of the information coming OUT (not necessarily going IN) to the low pass filter. Check out your communications theory textbook on this one. In terms of multiplying the signal by a modulating waveform, yes, this affects the spectrum of the result. The theory of sampling always begins by using a train of Dirac delta functions as the sampling waveform; Dirac delta functions are infintesimally short, impulses which do not exist in the real world but have nice flat spectral properties. Real world sampling waveforms are generally retangular because of the sample-and-hold circuits used in real A/D converters. Since the fourier transform of a rectangular pulse is a sinc (sin(x)/x) function, this has the effect of giving a sinc shape to the resulting spectrum. This is corrected in the player with an inverse sinc function which is added either to the CD low pass reconstruction filter or to the pre-sampling anti-aliasing filter, I'm not sure which one. Does anybody know? Phil