The goal is to design M analysis and synthesis FIR filters so that the analysis filters satisfy some frequency specifications and the filter bank(almost) meets the perfect reconstruction (PR) conditions. Both goals are achieved by minimizing the following performance index:
J=w1*(PR error)+w2*(Frequency Specification error)
where w1 and w2 are optional weights
The algorithm can be used to design both uniform (critically/over sampled) and non-uniform (with compatible as well as incompatible sampling set) filter banks. The method is based on the following report:
Moazzen, I. , Agathoklis, P., "A General Approach for Filter Bank Design Using Optimization", Technical Report, 2014.
This report can be downloaded from:
http://www.ece.uvic.ca/~imanmoaz/publications_files/Report.pdf In order to learn how you can use this toolbox, please copy all the m-files included in the "Filter Bank Design" folder into your current Matlab directory and type "help Filter_Bank_Design".