August 2013
Intermediate to advanced
360 pages
7h 23m
English
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Appendix 2: Sampling theorem
Sampling picks out values f(nT) from a signal f(t), at regular intervals. This is equivalent to the multiplication of f(t) with the signal s(t), given by the expression:
where (t) is a delta function.
The Fourier transform Fs(ω) of fs(t) is given by the expression:
where ωs= 2π/T. When two functions are multiplied in time their transforms in the frequency domain are convoluted. For this reason, the spectrum F(ω) is repeated at multiples of the sampling frequency. Function f(t) may be recovered from Fs(ω) by first multiplying ...
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