Basic Idea

The basic idea is to partition FFT bins into the desired nonuniform bands, and perform smaller inverse FFTs on each subband to synthesize downsampled time-domain signals in each band. A simple example for a length 8 FFT octave filter bank is shown in Fig.9.32. The remainder of this subsection presents the basic theory in a detailed development which retraces the reasoning leading to the idea. In keeping with an applied style, mathematical notation is largely avoided in favor high-level signal operations in matlab.

The next subsection begins with further explication of the (overly) simple example of Fig.9.32, followed by discussion of further refinements for achieving audio filter banks of more practical complexity and quality.

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Subsections

• Summing STFT Bins

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About the Author: 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.