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derivation as special cases of poission summation

derivation as special cases of poission summation

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it is apparent that when there is no overlap of the copies (aka "images") of X(f), the k = 0 term of Xs(f) can be recovered by the product:

where:

At this point, the sampling theorem is proved, since X(f) uniquely determines x(t).

All that remains is to derive the formula for reconstruction. H(f) need not be precisely defined in the region[B, fs ? B] because Xs(f) is zero in that region. However, the worst case is when B = fs/2, the Nyquist frequency. A function that is sufficient for that and all less severe cases is:

where rect(

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