newman (05/17/83)
I'd be interested in seeing some discussion of the adequacy of the 44.x kHz sampling rate in current compact disk players. Is it high enough for all audio purposes? Can someone familiar with the Nyquist frequency stuff give some input? The standard argument against seems to be "well a 20 kHz sine wave will only get sampled twice". Is this significant? Certainly the disks I've heard sound pretty impressive.
joel@decwrl.UUCP (Joel McCormack) (01/16/85)
Subject: CDs and sampling rates
Newsgroups: new.audio
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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!joelnewton2@ucbtopaz.CC.Berkeley.ARPA (01/16/85)
Any noodle-brained musings about physics (actually mathematics) that begin "Elementary physics aside..." have written their own epitaph. Considering the aggregate resources of people on this net, wouldn't it be great if the "informative" postings were from people who *know* and the inquisitive postings were from people who want to learn, instead of the other way around? Or should this be posted to net.utopia? Grumpily, Doug Maisel
herbie@watdcsu.UUCP (Herb Chong [DCS]) (01/24/85)
In article <232@decwrl.UUCP> joel@decwrl.UUCP (Joel McCormack) writes: >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. you obviously don't remember a whole lot about Fourier transforms. Fourier proved that ANY causal signal can be represented as an infinite sum of sine (or cosine) waves. music certainly is a causal signal and a Fourier transform is a complete representation of any such signal. whether the signal is periodic or not is irrelevant. it just changes the limits on the Fourier integral. BTW, for those who read my posting of BAUD vs. bits/s, i apologize for having the definitions exactly reversed. Herb Chong, BASc Computer Consultant I'm user-friendly -- I don't byte, I nybble.... UUCP: {decvax|utzoo|ihnp4|allegra|clyde}!watmath!water!watdcsu!herbie CSNET: herbie%watdcsu@waterloo.csnet ARPA: herbie%watdcsu%waterloo.csnet@csnet-relay.arpa NETNORTH, BITNET, EARN: herbie@watdcs, herbie@watdcsu POST: Department of Computing Services University of Waterloo N2L 3G1 (519)885-1211 x3524