Sep 21, 2017 term paper 2

SHANNON’S SAMPLING THEOREM. SUPPOSE THAT H IS A CONTINUOUS SIGNAL DE- FINED ON THE INTERVAL…

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Shannon’s sampling theorem. Suppose that h is a continuous signal de- fined on the interval [−T/2,T/2] of length T . Then, from equations (10.1) and (10.2)

The sequence of coefficients, an n∈Z, is called the Fourier transform h of h, i.e., h(n) = an. If, instead of being defined on some finite interval, h is defined on all of R then it may still have a Fourier transform.23 Generally, to synthesize such a signal we need to use basic signals of all frequencies

A signal h : R → R is called “band-limited” if for some frequency fc, its Fourier transformh( f ) = 0 whenever |  | > fc, that is, if h is composed of only a finite range of frequencies.


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