Research On The Design&Application Of All-Phase Digital Filter With Window

This dissertation deals mainly with windowed overlapping digital filter in transform domain, including its application in adaptive signal processing,design of 2-dimensional filtering template,spectrum analysis and multiresolution analysis of image, etc. First, the paper presents a novel N-order overlapping digital filter with front and back windows in frequency domain—all phase digital filter(APF), which output equals to the mean of sum of outputs from the system with N fragmentary inputs relevant to the signal at some time. Based on this module, some other notions as APF in DCT domain,DWA and DST domain are advocated as well. And the corresponding FIR modules are theoretically deduced out respectively, as well as proposing no-window,single-window and dual-window system. It can be verified by experimental results that all phase digital filter successfully eliminates the distortion resulting from truncating, with much better effect than fragmentary processing.Secondly, the conditions for strict linear phase,sampling theorem in frequency domain of AOF system are presented in detail through analysis of its amplitude and phase characteristics to frequency. In order to promote the performance of AOF system, two algorithms on how to efficiently design the window, one of which is based on LMS principle and the other is bifurcating of rectangle window which treats the system window as being formed from the convolution of two lower-ordered rectangle window on the left and right branch of the dichotomic tree and therewith forms multilevel decomposition via recursion, are put forward. Experimental results have shown AOF system with such window function not only decreases the ripples over both pass and stop bands, but also can achieve far lower stopband attenuation than average.Thirdly, by the analysis of essence of filtering of AOF, a new algorithm of windowed overlapping(WO) is advanced. By exploiting WO in adaptive signal processing, two new algorithms in both time domain known as WO-LMS and transform domain known as WO-TLMS are developed. Results of experiment about adaptive recognition indicates that this algorithm bears such two merits as faster convergence speed and lower steady error than conventional LMS. Applying WO-LMS algorithm in spectrum analysis,module designing and multiresolution analysis respectively gives birth to favorable results.Finally, by making use of the SIMULINK module in software MATLAB, functions and fine performance of AOF are validated in the simulation.