A Discussion of Sampling Theorems

The convolution theorem of Fourier analysis is a convenient tool for the derivation of a number of sampling theorems. This approach has been used by several authors to discuss first-order sampling of functions whose spectrum is limited to a region including the origin ("low-pass" functions). The present paper extends this technique to several other cases: second-order sampling of low-pass and band-pass functions, quadrature and Hilbert-transform sampling, sampling of periodic functions, and simultaneous sampling of a function and of one or more of its derivatives.