How can discrete Fourier transform (DFT) algorithms be optimized for real-time audio signal processing?

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Ian Dash

The short answer is the Fast Fourier Transform, published by Cooley and Tukey in 1965 - see https://en.wikipedia.org/wiki/Fast_Fourier_transform . Texts on codec theory also detail variations on this idea, such as the discrete cosine transform and wavelets. Google AI says popular textbooks for codec theory include "Modern Coding Theory" by Richardson and Urbanke, "Introduction to Coding Theory" by Roth, and "A First Course in Coding Theory" by Hill.

Vladimir Kubov

Your question corresponds to a point from a classic lecture course on periodic signal analysis. It's unclear why you're asking it in such a generalized form ;)