The Sampling Theorem and Shannon’s Formula

Abstract

Shannon’s formula is an interpolation formula that expresses the value f(t) of a signal at any time t in terms of its values f(na) at the discrete points na, n ∈ ℤ. The signal f is thus completely determined by the sampled signal af Δ _a . This is what we had in mind when we mentioned in the last lesson that sampling does not destroy information. Since this property is patently false for arbitrary signals, some restrictive assumptions must be made about f. Our point of departure will be Poisson’s formula (37.7); thus the first assumption is that f is band limited.