M-Channel Uniform Linear Phase Filter Banks And Wavelet-like Filter Banks

In the past decades, multirate digital filter banks attract many attentions in various fields, such as speech, image and communication applications. Filter banks with linear phase (LP) property is highly desired in image processing. The existed methods for the design of M-channel uniform LP filter banks are focus on the perfect reconstruction (PR) property. They are complicated and have some limitations. While in some applications, small distortion can be tolerated. Filter banks with near-PR (NPR) property is sufficient. Thus, simple methods with good filter quality are more expected.This thesis firstly investigates the M-channel uniform LP filter banks, and proposes a new design method based on the Parks-McClellan algorithm. By using this method, the requirements imposed on the entire filter bank are simplified as those on individual filters. Thus it greatly reduces the design of the filter banks. Furthermore, system with good filter quality can be achieved. Additionally, it is more flexible in choosing the filter length and the number of channels.Based on the M-channel LP filter banks, we further research on the wavelet theory and present a new method to design LP wavelet-like filter banks. It is based on LP NPR filter banks obtained by modulation technique. By imposing the regularity condition realized by FIR notch filter on such NPR filter bank, the LP wavelet-like filter banks can be obtained. The resulted sysytem preserves good filter quality, such as high stopband attenuation of the original NPR filter bank. Furthermore, our method has low design and implementation complexity due to the modulation technique.Finally, we spread our study to 2D filter banks. Since filter banks with non-LP property produces artifacts in image processing, we propose a phase compensation technique for the non-LP system, aiming at solving this problem. By adding a phase function on each filters of the original non-LP filter bank, the phase nonlinearity of each filter is compensated, and the distortion caused by the non-LP system can be eliminated in the image processing. This phase compensation method provides a relatively loose circumstance for the design of LP filter banks.