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Some of Shannon's better known known theorems include
the Sampling Theorem, which indicates that a bandwidth-limited
signal can be reconstructed only if sampled at least at twice
the frequency of the highest-frequency spectral content.
Take a 1 Vpp@40Hz Sinewave, highest-frequency spectral content is 40Hz,
sample it at twice this frequency, 80Hz, sample at 0 and 180 degrees (0Vpp
Amplitude), the reconstructed sinewave will be 0Vpp at 0 Hz. Oh well, guess
Shannon's theorem is incorrect...
Picking on a dead guy, how charming. Personally when I took the time to see
how Shannon is right, a whole batch of light bulbs of understanding the
digital audio process lit up.