MUS421 Lecture 8A
FFT Signal Processing: The Overlap-Add (OLA) Method for Fourier Analysis, Modification, and Resynthesis

Julius O. Smith III (jos at ccrma)
Center for Computer Research in Music and Acoustics (CCRMA)
Department of Music, Stanford University

Detailed Contents (and Navigation)

• Frequency-Domain Convolution
• FFT Convolution
  • Audio FIR Filters
  • Zero Padding for Acyclic FFT Convolution
  
  
• FFT Convolution Example 1: Low Pass Filtering
  • Example 1: Input Signal
  • Example 1: FIR Filter Design
  • Impulse Response $h$
  • Impulse Response and Amplitude Response
  • Prepare for Frequency-Domain Convolution
  • Perform Frequency-Domain Convolution
  • Return to Time Domain
  • Zoom-In on Start-Up Transient
  
  
• Example 2: Time Domain Aliasing
• FFT Convolution Across Frames
  • Overlap-Add Signal Decomposition
  • Example Overlap-Add Decomposition
  • Constant Overlap-Add (COLA) Constraint
  • COLA Windows
  • Modified-Hamming Overlap-Add Example
  • Oversampled Perfect Reconstruction Filter Banks
  • COLA Window and Hop-Size Examples
  • Periodic Windows
  
  
• Example 3: Overlap-Add Convolution
  • Frame 1, OLA Example 3
  • Frame 2, OLA Example 3
  • Penultimate Frame, OLA Example 3
  • Final Frame, OLA Example 3
  
  
• OLA Summary
  • OLA Summary, Cont'd
  • OLA Summary, Cont'd
  
  
• Quick Summary of Zero Padding
• Overlap-Save Method
• Time Varying Modifications
  • Block Diagram Interpretation
  
  
• Weighted Overlap Add
  • Weighted OverLap Add (WOLA) Procedure
  • When to Use Weighted Overlap-Add
  • Choice of WOLA Window
  • WOLA Window Construction
  
  
• WOLA Applications
• Poisson Summation Formula Derivation
  • Poisson Summation Formula
  • Strong COLA
  • Weak COLA
  • PSF Dual and Graphical Equalizers
  • Ideal Graphical Equalizers
  
  
• About this document ...