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.