The comb signal and its Fourier transform

Abstract

In this paper, we study the aperiodic comb signalfrom the point of view of the Fourier transform. The comb is very important in the theory of ideal sampling. The knowledge of its properties is crucial for the establishment of suitable interpolation schemes. Here, we present sufficient conditions so that the Fourier transform of an aperiodic comb is an aperiodic comb. We use this result to propose: (1) an alternative approach to the de"nition of an almost periodic signal and its anharmonic Fourier series; (2) a generalisation of the Shannon}Whittakker sampling/reconstruction for the irregular sampling case. Application of this theory to pulse duration modulation and pulse position modulation is also presented.