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 18. FFT: Decimation-in-Frequency Algorithms
Decimation-in-time FFTs are based on repeatedly splitting the DFT summation into two summations—one for the decimated time sequence from which even-indexed samples have been removed and one for the decimated time sequence from which odd-indexed samples have been removed. As the name implies, decimation-in-frequency FFTs split the DFT summation in a way that produces decimated frequency sequences. The DFT summation can be specialized for computing only the even-indexed frequency samples:
18.1
After some algebraic manipulations, Eq. (18.1) can be put in the form
18.2
where a[n] is the sequence ...
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