New Design and Factorization Methods for Perfect Reconstruction Causal Stable Iir Filter Banks

This dissertation, "New Design and Factorization Methods for Perfect Reconstruction Causal Stable IIR Filter Banks" by Shishu, Yin, 殷仕淑, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled New Design and Factorization Methods for Perfect Reconstruction Causal Stable IIR Filter Banks Submitted by Yin Shishu for the degree of Doctor of Philosophy at the University of Hong Kong in November 2006 Filter Banks (FBs) have important applications in speech, audio, image and array processing. This thesis is concerned with the theory, design and factorization of causal stable infinite impulse response (IIR) FBs in both two-channel and M-channel cases. The design of perfect reconstruction (PR) or nearly perfect reconstruction (NPR) FBs is usually obtained by iterative procedures involving nonlinear constrained optimization. When the number of variables and constraints increases, the optimization procedure is rather sensitive to the initial value of FBs, especially for cases with low reconstruction delay. In this thesis, a new method for designing two-channel and M-channel NPR finite impulse response (FIR) FBs is presented. These FBs are designed to have an approximate cosine rolloff transition band so that the flatness conditions are automatically satisfied. The design problem can be formulated as a convex optimization problem. NPR FIR FBs so designed have a reasonably low reconstruction error and good frequency performance. Then, they are used as the initial guess for further optimization to obtain high quality PR FIR FBs. A new modified model reduction technique for designing NPR IIR FBs is presented. The polyphase components of these FBs are designed to have an identical denominator. Hence, the PR condition is considerably simplified. Another advantage of the proposed method is that the stability of the IIR filters is guaranteed and the NPR IIR FBs so obtained can be used as the initial guess for designing PR IIR FBs. To preserve the PR property after coefficient quantization, a new factorization technique of two-channel and M-channel IIR FBs is proposed. The proposed factorization is based on the lifting scheme and the implementation complexity is reduced by an approximate factor of two. Using these results, the resulting IIR FBs become PR structurally. Since the factorization is highly non-unique, a new method is further developed to select the factorization which has a smaller dynamic range of the lifting coefficients. The small dynamic range is very useful to the multiplier-less realization of IIR FBs whose lifting coefficients can be implemented as canonical signed digits (CSD) or sum of powers of two (SOPOT) coefficients. Because of the reduced arithmetic complexity, this approach is very attractive for VLSI implementation. To offer more flexibility in time-frequency partitioning and better performance in applications such as signal analysis and coding, a new class of NPR low-delay (LD) FIR and IIR recombination nonuniform FBs (RNFBs) is proposed. To suppress the spurious response possibly found in the stopband of the resulting analysis filter in the LD FIR RNFB, a matching condition between the original uniform FB and the recombination FB is developed. The general NPR IIR RNFB can be obtained by converting the resulting LD FIR RNFB using the modified model reduction technique mentioned earlier. Since there are a large number of variables for designing general M-channel IIR RNFBs, it is difficult to satisfy both PR and stability constraints. Therefore, CMFBs are considere