November 2010
Intermediate to advanced
288 pages
8h 34m
English
book
Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation
by C. Britton Rorabaugh
Content preview from Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation
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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 ...
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