The Scientist and Engineer's Guide to
Digital Signal Processing
By Steven W. Smith, Ph.D.

Chapter 12: The Fast Fourier Transform

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.

• Real DFT Using the Complex DFT
• How the FFT works
• FFT Programs
• Speed and Precision Comparisons
• Further Speed Increases