ballstoall said:
pls explain... i didn't get what you said about "a lot of power" beyond
22.05kHz...?
i mean, shouldn't there be a difference in the frequencies of recorded
and real time?
Not until you get to the cut-off frequency for a particular
arrangement. If you look below 22.05kHz, you will see essentially
identical images. But for frequencies above 22.05kHz, the
straight-analogue signal will show some power (you will see a bit of
fuzziness there on the spectral analyzer), whereas for the digitally
processed signal, you will see a drop-to-zero. Here's what's
happening:
If you take the straight-analogue signal, and view its spectral
content, you will most likely see components in the lower frequences
(under 20kHz), as well as components at higher frequencies (above
20kHz).
If you look at the recorded signal, assuming that the spectral content
of whatever was recorded also had frequency components higher than
20kHz, you will *not* see those higher components in the analogue
output of the digitally processed signal. The reason has to do with
filtering. To reconstruct an analogue signal perfectly, the rate of
sampling must be at least twice the highest frequency component
contained in the sampled signal. So if someone plays high-pitched
music, and the highest frequency component in that music is 8 kHz, then
one must operate the A/D converter at at least 16 kilosamples per
second (kps) for perfect reconstruction which is equivalent to avoiding
spectral overlap in the frequency domain. This is the essence of the
Nyquist Sampling Theorem, and this theorem is directly related to what
is really happing when you sample a signal and later convert it back to
analog - when you sample the signal in the time domain, with the
*intent* to regenerate the analogue signal, you should think in your
mind, at each instant of sample, BAM!!! You are multiplying the signal
with a sequence of impulses, where each impulse is a BAM! Then, to see
what this combination of multiplied signals makes in the frequency
domain, you must convolve the image of the sampled signal in the
frequency domain with the Fourier Transform of the "BAM" signals,
which, in the frequency domain, is yet another train of impulses, but
scaled by a factor. To keep the resulting blobs from overlapping each
other, the spacing between the impulses in the time domain must be very
narrow, or equivalently, very wide in the frequency domain. But "very
wide" is relative - if a signal is sufficiently band-limited for a
particular spacing of the impulse train in the frequency domain, then
no overlap will occur during convolution. To band-limit the signal,
you must use an anti-aliasing (low-pass) filter before sampling to kill
off any frequencies higher than 22.05 kHz, and another similar filter
at the output.
So if you are listening to a signal that is analogue throughout the
channel, it *could* have components higher than 22.05kHz. But if
you're listening to a signal that has been low-pass filtered, digitally
sampled (A/D), converted back to analog (D/A), and low-pass filtered
again, you can be certain that components above 22.1kHz have been
essentially killed off. For a digitally processed signal, anything
beyond 22.05kHz will be due to noise and imperfections in the output
filter itself, and should barely show up on a spectral analyzer.
It should come as no suprise to you that 22.05 kHz (44.1 ksps) is the
cut-off frequency. It just happens to be near the threshold of hearing
for many humans.
-Le Chaud Lapin-
