Mathematical Tutorial of Discrete-Time Analysis of Sampling Rate Changing Concept for Digital Signal Processing and Digital Communication Prospective
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Abstract
Greatly demanding on digital signals (or Discrete-Time (DT) signals), which are generated from Continuous-Time (CT) signals by a sampling process based on Nyquist-Shannon theorem, for modern digital processing such as Digital Signal Processing (DSP) and digital communication, the concept of sampling rate changing by an integer factor and a non-integer has been extensively investigated for one and a half decade. Thereby, this article introduces the mathematical tutorial of DT analysis of sampling rate changing concept for both an integer factor and a non-integer. This article first algebraically presents the down-sampling concept with an integer factor and later algebraically presents the up-sampling concept with an integer factor. Next, the article algebraically presents the sampling rate changing concept with a non-integer factor for both down-sampling and up-sampling by using the combination of down-sampling concept and the up-sampling concept. In addition, the several examples of the down-sampling with an integer factor, the up-sampling with an integer factor and the sampling rate changing concept with a non-integer factor, which are disclosed in each algebraically detail, are introduced for bring the reader comprehensively recognizing.
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