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## RE: Questions for audio gurus

 Subject: RE: Questions for audio gurus Tom Duff <> Thu, 23 Feb 2006 09:56:43 -0800 (PST)
 ```"Don Lloyd" says: > I'm not sure I understand this here Nyquist limit. Wouldn't > the sampling frequency have to be _much_ greater than > twice the highest frequency being recorded? F'rinstance, > say you want to record a 22.05KHz sine wave. The best you > could do with a 44.1KHz sample rate is a 22.05KHz square > wave, regardless of bit depth. The quantitative frequency > would be present, but in a considerably altered shape. It depends on what your recording and playback systems do with the samples. If each sample value denotes setting the signal level to a particular value and holding it at that level until the next sample comes along, then, indeed, you can represent 22.05 KHz square waves and not sines. But playback systems (invariably?) include anti-aliasing filters (if only to protect your power amplifiers and speakers from high-frequency signals that they probably weren't designed to deal with), which round off the corners of the signal and introduce a certain amount of ringing. An "ideal" anti-aliasing filter converts an single-sample impulse (i.e. a sequence of samples all but one of which are zero) into a signal which looks like sin(44100 PI t)/(44100 PI t), which is a sinusoid of frequency 22.05 KHz that falls off on either side of the sample position. This signal is usually called the "sinc function." If you add up a bunch of sinc functions, each delayed and scaled according to your recorded samples, you will find, after slogging through more math than either of us is probably interested in, that you can indeed represent a 22.05 KHz sine wave. In fact, because 22.05 KHz is right on the hairy edge of what the Nyquist thm says you can represent, its phase had better be exactly right in order for the reconstruction to work. But for any lower frequency, even 22.04999999 Khz, you can, regardless of phase, exactly reconstruct the signal from its samples. All of this depends on being able to use an ideal sinc reconstruction filter. As you might suspect, real-world filters can only approximate ideal filters, so real-world systems, while they can, with enough care, come very close, must invariably fall short of ideal performance. -- Tom Duff. ``My favorite country musician'' -Eric Clapton ________________________________________________________________________ ________________________________________________________________________ ```
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