Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site decwrl.UUCP Path: utzoo!watmath!clyde!bonnie!akgua!sdcsvax!sdcrdcf!hplabs!hpda!fortune!amdcad!decwrl!joel From: joel@decwrl.UUCP (Joel McCormack) Newsgroups: net.audio Subject: CD sampling rates Message-ID: <232@decwrl.UUCP> Date: Tue, 15-Jan-85 18:12:08 EST Article-I.D.: decwrl.232 Posted: Tue Jan 15 18:12:08 1985 Date-Received: Thu, 24-Jan-85 19:25:02 EST Organization: DEC Western Software Lab, Los Altos, CA Lines: 61 Subject: CDs and sampling rates Newsgroups: new.audio ---------- I have wondered about sampling rates in CDs for quite awhile. My conclusion: the sample rate, elementary physics classes aside, really is too low for fairly "precise" reproduction of music. But not having higher sampling rates to compare against, I don't know what difference it makes. CDs sure SOUND good! First, the sampling rate should be strictly greater than twice the highest frequency. Given a 40,000 Hz. sampling rate, if only zero- crossings are sampled all you really know is that there is a 20,000 Hz component with an amplitude >= 0. Big deal. If the sampling rate is strictly greater than twice the highest frequency, then MATHEMATICALLY I understand how (given a perfect world), both the freqency and amplitude can be reconstructed (given that the freqency in question is a sine wave). I also understand Fourier transforms make it possible to reconstruct lower frequencies with partials that are less than half the sampling rate. Unfortunately, I see two things wrong with this in the CD world: 1) Music waveforms are NOT sine waves, nor are they COMPOSED of sine waves. Sine waves go on forever, while music changes. All that stuff you learned about Fourier transforms is only approximately related to music (on the assumption that sharp transitions take place relatively infrequently to the cycle time, and that (aside from sharp attacks) amplitude envelopes look fairly flat against cycle time). But just because true SINE waves can theoretically be recovered by sampling higher than the Nyquist frequency DOES NOT imply that music (or for that matter, any PHYSICAL sort-of-periodic sort-of-waves) can be recovered. 2) Ignoring 1), I am not sure how well circuits in CD players actually convert the digital to accurate analog representations of the original waveform. I am not questioning the accuracy of DA converters, but rather what circuits (and how accurately) extrapolate the proper amplitude for frequencies that are quite close to half the sampling rate? Just what DOES a waveform stored as 000 000 001 -001 002 -002 .... 999 -999 ... 000 000 get reproduced as? I would bet money that rather than noticing how fast the deviations from 0 were increasing (and eventually, decreasing), and then putting the proper constant-amplitude sine waveform into your preamp, a CD player instead overlays an amplitude beat on the frequency being reproduced. Note that even if it were possible to compute the proper amplitude, the roundoff error for numbers close to zero would probably screw things up anyway. What difference does this make? I don't know. From what I know of psycho-acoustics, I imagine not a lot. Frequencies very close to 22 KHz. are not that noticable to most people, so very slow beats (say .2 to 1 seconds) probably won't be noticed, except in artificial conditions designed to point out these sorts of defects. Unless that is the ONLY frequency being played in the test, and pretty loud at that, it's going to be masked. And lower frequencies subject to this phenomenon are going to have an amplitude beat of a high enough frequency that it will be even less noticable. Joel McCormack {ihnp4!decvax!ucbvax}!decwrl!joel