Note 5. Delta Functions and the Sampling Theorem
When ideal sampling is viewed as a direct mapping process, as it is in Note 3, the creation of spectral images is simply stated as a fact and accepted without mathematical justification. To generate mathematical support for the existence of these images, a more complicated mathematical model of the sampling process must be adopted. In addition to correctly predicting the appearance of spectral images, such a model can also be used to derive the discrete-time Fourier transform (DTFT) and the discrete Fourier transform (DFT) from the “usual” continuous-time Fourier transform (CTFT). (See Math Boxes 12.1 and 13.2.)
If the result of ideal sampling is considered in the continuous-time domain, each ...
Get Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
