In chapter 6, we investigated the definition and properties of the discrete-time Fourier transform X(e jω ), with ω being a continuous frequency variable, and found it to be very useful for analyzing a wide variety of signals and systems of theoretical interest. However, much of the practice of digital signal processing is done in computers where we cannot evaluate a continuum of frequencies ω, nor can we input and store an infinite-duration sequence x(n). Hence, for actual data sequences, as opposed to theoretically defined signals, we cannot compute the Fourier transform, in general.
KeywordsDiscrete Fourier Transform Chinese Remainder Theorem Hanning Window Rectangular Window Circular Convolution
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