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An important aid in the analysis and display of speech is the sound spectrogram, which represents a time-frequency-intensity display of the short-time spectrum. 1-3 With many modern speech facilities centering around small or medium-size computers, it is often useful to generate spectrograms digitally, online. The fast Fourier transform algorithm provides a mechanism for implementing this efficiently.
Alan V. Oppenheim (Sat,) studied this question.