A generalized STFT may be defined by 
This filter bank and its reconstruction are diagrammed in Fig.11.35.
The analysis filter is typically complex bandpass (as in the STFT case). The integers give the downsampling factor for the output of the th channel filter: For critical sampling without aliasing, we set . The impulse response of synthesis filter can be regarded as the th basis signal in the reconstruction. If the are orthonormal, then we have . More generally, form a biorthogonal basis.
Dyadic Filter Bank Design