Filtering Property of Signal Sampling in General and Under-Sampling as a Specific Operation of Filtering Connected with Signal Shaping at the Same Time

In this paper, we show that signal sampling operation can be considered as a kind of all-pass filtering in the time domain, when Nyquist frequency is larger or equal to maximal spectrum sampled. We demonstrate seemingly obvious observation has wide-ranging implications. They are discussed here detail. Furthermore, discuss also shaping effects occur case under-sampling. That is, smaller than Further, explain mechanism specific distortion arises under these circumstances. call it shaping, not aliasing, because many reasons throughout paper. Mainly however fact behind it, called here, usual sense. And, shown depends upon phase. formulated other words, viewed one which shapes and performs low-pass at same time. Also, an interesting relation connecting Fourier transform filtered with use ideal filter having cut lying region under-sampling transforms its two under-sampled versions derived. This presented too.