Julius wrote:
> As the WhittakerNyquistKotelnikovShannon sampling theorem
states;
> When sampling a bandlimited 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.
> </snip>
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 frequencydomain spectrogram analysis) that
exhibits an upper limit of less than 20 kHz. Therefore, we cannot
distinguish a highfrequency (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 lowpass filter at the output
of the D/A converter. Highquality 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
highfrequency 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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