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[OFFLINE DEMO - Orignial by Don Johnson]Discrete Fourier Transform (DFT)

Module by: Eric Wang

Summary: The Fourier transform can be computed in discrete-time despite the complications caused by a finite signal and continuous frequency.

The discrete-time Fourier transform (and the continuous-time transform as well) can be evaluated when we have an analytic expression for the signal. Suppose we just have a signal, such as the speech signal used in the previous chapter, for which there is no formula. How then would you compute the spectrum? For example, how did we compute a spectrogram such as the one shown in the speech signal example? The Discrete Fourier Transform (DFT) allows the computation of spectra from discrete-time data. While in discrete-time we can exactly calculate spectra, for analog signals no similar exact spectrum computation exists. For analog-signal spectra, use must build special devices, which turn out in most cases to consist of A/D converters and discrete-time computations. Certainly discrete-time spectral analysis is more flexible than continuous-time spectral analysis.

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