Research On The Design And Applications Of Filter Banks

This paper discusses the design and applications of filter banks, with emphasis on design of linear phase perfect reconstruction filter banks and its application in image denoising. It consists of several parts as follows:In the first part, after an introduction of basic theory and history of filter banks, an analysis of lattice structure filter banks is given. The requirements of perfect reconstruction and linear phase are discussed and some constrains of filter length and symmetry property are analyzed in details. Besides, relative designing practice and examples are given.Part two is contributed to the analysis of filter banks in time domain. The representation of each part in filter banks and the perfect reconstruction conditions are introduced here. Then the design procedure in time domain and several examples are presented.Based on the design methods above, we research the possibilities of build nonuniform filter banks with linear phase in the third part, pointing out the difficulties may occur and bringing up our ideas.In part four, a new method of design linear phase filter banks with SOPOT(Sum of Powers of Two) coefficients is presented on the basis of perfect reconstruction lattice structure filter banks. And a design example is given to prove the efficiency of this method.The fifth part is a research of application of filter banks in the image denoising. A new denoising method with optimized threshold is introduced, whose efficiency has been certified by some comparing examples.Finally come the summary of above work and a forecast of future research.