Jerome Fine replies: Actually, that is exactly what I helped an acoustical engineer do about 10 years ago (so this reply is on-topic). The goal was the analyse the sound reduction properties of a box around a large compressor station (pumping oil or natural gas). The requirement was to reduce the noise level from the station to below the ambient outside noise level when the measurement was taken over 100 yards away. Since a sound meter to measure a noise level normally can't measure the intensity of a sound which is below the background white noise, there seem to be two solutions: (a) Brute Force - bring in a train load of speakers and amplifiers to generate a sound loud enough to be heard above the ambient noise level at 100 yards not fit inside the station. (b) Intelligent Measurement with a computer using both A/D and D/A hardware along with that (sheesh) sampling of the required sine waves. If anyone wants further detail and needs to have this done for an actual application, I can refer you to the proper source. The key point is that the intelligent use of computer hardware and software was able to provide a solution that could actually prove that the acoustical shell (noise suppressing material) around the station reduced the noise produced by the compressor to a value which could not be heard by the normal human ear above the background noise when the person was over 100 yards away. And the only speaker that was used did not generate a sound louder than the noise level already inside the station. And that, my dear Virginia, is why sampling of sine waves is sometimes needed. Sincerely yours, Jerome Fine

You're right in that this isn't a forum for signal processing, but it's worth notice that the sample rate deterines the top-end cutoff frequency for the sample, and the epsilon (the difference between 2x the cutoff frequency) determines the resolution achievable with a finite length of sample. There are more factors at work than that, however, and if one were really interested in what's going on in processes such as this, one would simply read the Shannon work. Dick ----- Original Message ----- From: "Carlos Murillo" <cmurillo(a)emtelsa.multi.net.co> To: <classiccmp(a)classiccmp.org> Sent: Wednesday, February 28, 2001 12:08 PM Subject: RE: RZ,nI: Claude Shannon

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At 07:27 PM 2/28/01 -0700, you wrote: Nyquist came up with the "Nyquist frequency" in a slightly different (yet related) context. However, the formal proof and reconstruction technique is due to Shannon. Carlos.