6.8. The Discrete Fourier Transform (DFT)
We have already seen that the basis vectors/images for the KL and SVD expansions are not fixed but are “problem dependent” and are the result of an optimization process. This is the reason for their optimality with respect to the decorrelation and information-packing properties. At the same time, this accounts for their major disadvantage, that is, their high computational complexity. For the rest of the chapter we will be concerned with transforms that use fixed basis vectors/images. Their suboptimality with respect to decorrelation and information packing properties is most often compensated by their low computational requirements.
6.8.1. One-Dimensional DFT
Given N input samples x(0), x(1),…, ...
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