Appendix B: Filterbank Design
2004
Filterbank DesignIn this section the design of prototype lowpass filters for oversampled, DFTmodulated polyphase filterbanks is described.For this type of filterbank the aliasing terms can be kept small, making them well suited for the application of echo and noise control.Among a variety of design procedures' we have chosen the one presented in [231,236].The design process can be divided into four parts: 0 First, conditions for a perfect reconstruction of the incoming signal after passing the analysis-synthesis system are derived.During this derivation it will be assumed that no subsampling is applied; accordingly, the aliasing terms can be neglected.0 We will see that the conditions for perfect reconstruction specify only the convolution of the analysis and synthesis prototype impulse responses = gz *& (and not the filter coefficients themselves).The restrictions can be fulfilled with a simple product of two functions $ ~, i and $ ~, i .The first one satisfies the reconstruction condition, while the second one can be designed to minimize aliasing components.'See [230] for details as well as the references cited there.