Downsampled STFT Filter Banks

We now look at STFT filter banks which are downsampled by the factor . The downsampling factor corresponds to a hop size of samples in the overlap-add view of the STFT. From the filter-bank point of view, the impact of is aliasing in the channel signals when the lowpass filter (analysis window) is less than ideal. When the conditions for perfect reconstruction are met, this aliasing will be canceled in the reconstruction (when the filter-bank channel signals are remodulated and summed).

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Subsections

• Downsampled STFT Filter Bank
  • Filter Bank Reconstruction
  
  
• Downsampling with Anti-Aliasing
  • Properly Anti-Aliasing Window Transforms
  • Hop Sizes for WOLA
  
  
• Constant-Overlap-Add (COLA) Cases
  • Hamming Overlap-Add Example
  • Periodic-Hamming OLA from Poisson Summation Formula
  • Kaiser Overlap-Add Example

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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.