Inverse DFT and the DFT Filter Bank Sum

The Length inverse DFT is given by [243]

This suggests that the DFT Filter Bank can be inverted by simply remodulating the baseband filterbank signals , summing over , and dividing by for proper normalization. That is, we are led to conjecture that

This is in fact true, as we will later see. (It is straightforward to show as an exercise.)

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Order a Hardcopy of Spectral Audio Signal Processing

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.