FFT Filter Banks

This section, based on [250], describes how to make practical audio filter banks using the Short Time Fourier Transform (STFT). This material bridges the filter-bank interpretation of the STFT in Chapter 8 and the discussion of multirate filter banks in Chapter 10. The filter banks of this section are based entirely on the STFT, with consideration of the basic Fourier theorems introduced in Chapter 2. In Chapter 10, filter banks such as used in audio compression are addressed. However, when not doing compression, i.e., when each channel of the filter bank does not have to be critically sampled, the methods of this section may suffice in many applications.

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Subsections

• Audio Filter Banks
• Basic Idea
  • Summing STFT Bins
  
  
• Inverse Transforming STFT Bin Groups
  • Improving the Channel Filters
  
  
• Fast Octave Filter Banks
  • Spectral Rotation of Real Signals
  • Improving the Octave Band Filters
  • Aliasing on Downsampling
  • Restricting Aliasing to Stopbands
  • Optimal Band Filters

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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.