Spectrum Aliasing Does not Occur in Case of Ideal Signal Sampling

Abstract

A new model of ideal signal sampling operation is developed in this paper. This model does not use the Dirac comb in an analytical description of sampled signals in the continuous time domain. Instead, it utilizes functions of a continuous time variable, which are introduced in this paper: a basic Kronecker time function and a Kronecker comb (that exploits the first of them). But, a basic principle behind this model remains the same; that is it also a multiplier which multiplies a signal of a continuous time by a comb. Using a concept of a signal object (or utilizing equivalent arguments) presented elsewhere, it has been possible to find a correct expression describing the spectrum of a sampled signal so modelled. Moreover, the analysis of this expression showed that aliases and folding effects cannot occur in the sampled signal spectrum, provided that the signal sampling is performed ideally.