Listening to music with incorrect sampling frequencies
If we want to reconstruct a continuous-time signal from a
discrete-time signal, knowledge of the sampling frequency is
critically important, since without it, we do not know to which real
time each time index corresponds. For example, music recorded on a CD
is stored as a sequence of numbers. By international agreement, all
music stored on CDs is sampled at 44.1 kHz; without this critical
piece of information, the stored music could not be faithfully
reconstructed in the continuous-time domain (on your stereo). Computer
music files, such as mp3's, have their sampling frequency encoded in
the file itself. If the encoded sampling frequency in the mp3 file is
incorrect for some reason, the music that your computer would play
would sound either too fast or too slow. To demonstrate this point, I
took a short piece of music (from Kenny Roger's "The Gambler"),
sampled at 32kHz, and played the original music during class, assuming
that the sampling frequency was 24kHz (incorrect), 32kHz (correct) and
40kHz (incorrect). The piece of music played back with the incorrect
sampling frequency of 24kHz sounds slowed down, while it sounds sped
up with the incorrect sampling frequency of 40kHz. Below are the music
files played during class.
Kenny Roger's "The Gambler" (23 sec.)
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Assumed sampling rate
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Music files
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24kHz (incorrect)
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(mp3, 244 kb)
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(wav, 724 kb)
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32kHz (correct)
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(mp3, 184 kb)
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(wav, 724 kb)
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40kHz (incorrect)
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(mp3, 148 kb)
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(wav, 724 kb)
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Last updated February 3, 2003 by Michael C. Nechyba