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The Scientist and Engineer's
Guide to Digital Signal Processing
by Steven W. Smith
California Technical Publishing
ISBN 0-9660176-3-3 (1997)
Chapter 12. The Fast Fourier Transform
- Real DFT Using the Complex DFT
- How the FFT Works
- FFT Programs
- Speed and Precision Comparisons
- Further Speed Increases
There are several ways to calculate the Discrete Fourier Transform (DFT), such as
solving simultaneous linear equations or the correlation method described in
Chapter 8. The Fast Fourier Transform (FFT) is another method for calculating the
DFT. While it produces the same result as the other approaches, it is incredibly more
efficient, often reducing the computation time by hundreds. This is the same
improvement as flying in a jet aircraft versus walking! If the FFT were not available,
many of the techniques described in this book would not be practical. While the FFT
only requires a few dozen lines of code, it is one of the most complicated algorithms in
DSP. But don't despair! You can easily use published FFT routines without fully
understanding the internal workings.
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