Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site unc.UUCP Path: utzoo!watmath!clyde!cbosgd!cbdkc1!desoto!packard!hoxna!houxm!whuxlm!akgua!mcnc!unc!rentsch From: rentsch@unc.UUCP (Tim Rentsch) Newsgroups: net.audio Subject: Re: CD reflections Message-ID: <81@unc.UUCP> Date: Sat, 19-Jan-85 16:07:49 EST Article-I.D.: unc.81 Posted: Sat Jan 19 16:07:49 1985 Date-Received: Wed, 23-Jan-85 07:50:42 EST References: Reply-To: rentsch@unc.UUCP (Tim Rentsch) Organization: CS Dept., U. of N. Carolina at Chapel Hill Lines: 28 Summary: In article jon@boulder.UUCP (Jon Corbet) writes: >[Finally! a use for my EE degree!] > >>From: rjn@hpfcmp.UUCP (rjn) >>HIGH END FIDELITY - If we assume (and perhaps we shouldn't) that all we >>need to capture are complex signals composed entirely of symetrical sine >>waves whose highest overtone is 20KHz, a (2x) digitizing rate in the >>vicinity of 40KHz just won't do. For example, suppose we digitize a >>pure 20KHz signal at 40KHz, and happen to capture only the >>zero-crossings. How much information does that get us? We need at >>least 3x digitizing (60 KHz) to reconstruct a pure sine wave, and I >>suspect that actual music demands that we use at least 4x (80 KHz). > > Wrong. In an ideal system, one needs to sample at no more than twice >the highest frequency component. This is known as the "Nyquist criterion." >In reality, one needs to go a little faster, since we have not invented the >perfect low pass filter yet...this is why CD's use something closer to 44K. >This is theoretically enough to reconstruct PERFECTLY any signal that does >not have components greater than 22KHz; by limiting themselves to 20KHz, >the CD makers are actually giving themselves some slop. > A small correction if I may. The nyquist theorem states that sampling at frequency 2F allows reconstruction of all information with frequency F or less, but only if the samples are infinite precision. Since finite precision (16 bits) is used, the actual fact is that information gets fuzzier (and so reconstruction gets worse) as the frequency gets closer to the nyquist limit.