Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83 v7 ucbtopaz-1.8; site ucbtopaz.CC.Berkeley.ARPA Path: utzoo!watmath!clyde!burl!ulysses!allegra!bellcore!decvax!ucbvax!ucbtopaz!newton2 From: newton2@ucbtopaz.CC.Berkeley.ARPA Newsgroups: net.audio Subject: Re: CD Reflections - 44.1k? Message-ID: <651@ucbtopaz.CC.Berkeley.ARPA> Date: Thu, 17-Jan-85 13:35:42 EST Article-I.D.: ucbtopaz.651 Posted: Thu Jan 17 13:35:42 1985 Date-Received: Sun, 20-Jan-85 01:48:17 EST References: <15100001@hpfcmp.UUCP> <3411@mit-eddie.UUCP> <1420@hplabs.UUCP>, <755@clyde.UUCP> Organization: Univ. of Calif., Berkeley CA USA Lines: 32 Here's a way to think about how the sampling theorem works, without needing to believe that "eventually" you need to sample a continuous repetitive waveform "everywhere" to be sure you get its peak amplitude. Actually, two ways: First, disabuse yourself of the notion that because music is transient-ridden or is characterized by an envelope that modulates (multiplies) a steady-state excitation, that therefore this implies the need for infinite bandwidth in a digital audio system. Yes, an impulse or discontinuous sinewave has a continuous spectrum that is not bandlimited, *but* the *premise* of the sampling theorem is that the signal is bandlimited to <1-2X the sampling rate. Thus, even if the acoustic signal is a spectral smear with non-zero magnitude in the nuclear phonon realm, *assume* that no significant components are present at more than <1-2X the sample rate. In practice, we use a big bad low-pass filter to attenuate such out-of-band signals sufficiently so the aliases resulting from their presence are less than an arbitrarily-decided bound. Second, even assuming continuous sinewaves, the system doesn't have to wait until it's tasted every chunk of a sinewave to know what frequency and magnitude it represents- this is the role of the complementary anti-imaging filter, which outputs, for example, a damped sinewave when excited by a pulse, or a continuous sinewave when excited by a pulse train, and selects only the first of the repeated ensemple of imaged spectra implied by discrete or stepwise output of the D/A. The real answer to nagging uncertainties about the propriety of hacking up the silken-smooth continuity of music is to settle on a bandwidth that is acceptable and then hack away; everything will bne provably copacetic *within those agreed-upon constraints*. It's not fair to keep coming back and claiming that things fall through cracks that never troubled anyone when we depended on even narrower-band media before digital. Regards, Doug Maisel