Perfect Reconstruction (PR) STFTs

We can consider $\hbox{\sc Cola}(R)$ and $\hbox{\sc Nyquist}(N)$ windows and window-transforms to be a routine requirement for a fixed-resolution time-frequency sampling system

Multiresolution time-frequency sampling systems may be created by

• Combining rectangular regions from fixed-resolution time-frequency samples
• Wavelet Filter Banks (invertible hence PR)
• Constant-Q Filter Banks (not PR, hence only approximately invertible)