Constant-Overlap-Add (COLA) Cases

• Weak COLA: Window transform has zeros at frame-rate harmonics:
  $$W(\omega_k) = 0, \quad k = 1,2, \dots, R-1, \quad \omega_k \isdef \frac{2\pi k}{R}$$
  • Perfect OLA reconstruction
  • Relies on aliasing cancellation in frequency domain
  • Aliasing cancellation is disturbed by spectral modifications
  • See Portnoff for further details
• Strong COLA: Window transform is bandlimited consistent with downsampling by the frame rate:
  $$W(\omega) = 0, \quad \vert\omega\vert \geq \pi/R$$
  • Perfect OLA reconstruction
  • No aliasing
  • better for spectral modifications
  • Time-domain window infinitely long in ideal case