Chapter 12
The Discrete Fourier Transform and Fast Fourier Transform Algorithms
In This Chapter
Looking at the DFT as uniformly spaced samples of the DTFT
Working with the DFT/IDFT pair
Exploring DFT theorems
Implementing the fast Fourier transform algorithm
Checking out an application example of transform domain filtering
Fourier’s name is associated with four different chapters of this book — nearly all the chapters in Part III. So what’s special about the discrete Fourier transform (DFT)? Computer computation! Under the right conditions the DFT returns a sample version of the discrete-time Fourier transform (DTFT) but using a systematic computer computation.
That’s right; the DFT allows you to move to and from the spectral representation of a signal with fast and efficient computation algorithms. You won’t find any integrals here! Complex number multiplication and addition is all there is to the mathematical definition of the DFT.
In this chapter, I introduce efficient methods ...
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