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## Re: Questions for audio gurus

 Subject: Re: Questions for audio gurus "Raimund Specht" <> Thu, 23 Feb 2006 10:27:30 -0000
 ```Julius wrote: > As the Whittaker-Nyquist-Kotelnikov-Shannon sampling theorem states; > When sampling a band-limited signal (e.g., converting from an > analogue signal to digital), the sampling frequency must be > greater than twice the input signal bandwidth in order to be able > to reconstruct the original perfectly from the sampled version. > Don wrote: > 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. Seems like the minimum sample rate would have > to be, oh, say, 5,644.8KHz. I agree that it is difficult to understand these things. However, I believe that it is important to note that our ears cannot be interpreted as a sampling system that simply analyzes the shape of the waveforms (you are correct that a sampled signal that is close to 22.05 kHz looks like a square wave in the digital domain). As far as I understand, our ears function like a filter bank (comparable to a frequency-domain spectrogram analysis) that exhibits an upper limit of less than 20 kHz. Therefore, we cannot distinguish a high-frequency (lets say 10 kHz) sine wave signal from a square wave signal of the same fundamental frequency. The upper harmonis of such a square wave (starting at 30 kHz) would just be inaudible to the human ear. Also note that the original shape of the audible part of such high- frequency signals is usually beeing reconstructed during playback. This reconstruction is performed by a low-pass filter at the output of the D/A converter. High-quality audio gear uses additional oversampling techniques that indeed use D/A converter clock rates that are much higher than the original sample rate. As a result, a high-frequency sine wave appears at the analog output of a CD player in a perfect sinusoidal shape (you might check that by using an oscilloscope). Regards, Raimund ________________________________________________________________________ ________________________________________________________________________ ```
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