engleski

Optimal Design of Perfect-Reconstruction and Nearly Perfect-Reconstruction Multirate Filter Banks

By using multirate filter banks, the signal under consideration can be separated in the frequency domain into two or more subband signals, each of them containing only one spectral part of the original signal. When applying various signal processing algorithms to these subbands, such as compression or denoising, significantly better performances may be achieved compared to the case where the same algorithms are applied to the original signal itself. Therefore, many modern digital signal processing algorithms are based on processing subband signals instead of directly processing the original signal. The crucial elements for this process are multirate filter banks. This thesis concentrates mainly on synthesizing multirate filter banks of two types, namely, alias-free two-channel filter banks and multi-channel (M-channel) filter banks. In the case of two-channel filter banks, the filter banks are first classified into various types and then design methods for filter banks based on the use of finite-impulse response (FIR) and infinite-impulse response (IIR) filters are proposed. The main emphasis is placed on methods for designing filter banks by minimizing the maximum of the stopband energies (least squares design) of the two analysis filters subject to the given passband and transitionband constraints and the given allowable reconstruction error. The proposed methods can be easily extended for minimizing the stopband ripples (minimax design) of the filters in the bank. Additionally, the properties of FIR filter banks designed by using the peak-constrained least squares optimization criterion are studied. This criterion provides a tradeoff between the least squares and the minimax criteria, which is very useful in some applications. In the case of M-channel filter banks, design methods for orthogonal (linear-phase) and biorthogonal (low-delay) cosine-modulated filter banks are proposed. The main emphasis is placed on cosine-modulated filter banks due to their efficient implementations and drastically reduced design complexity (only one prototype filter has to be designed) when compared to the direct design of M-channel filter banks. The design of perfect-reconstruction (PR) orthogonal filter banks can be further simplified by optimizing the angles of the lattice structures for the prototype filter instead of the prototype filter coefficients itself. Most of the methods introduced for designing prototype filters for cosine-modulated filter banks are based on a multistep design method. The design starts with a two-channel case, and then, in each step the number of channels is increased. The result of the previous step is modified and used as a startup solution for the next step. A noted exception is the design of PR biorthogonal filter banks that uses a state-of-the-art optimization technique called the second-order cone programming. For solving the constrained optimization problems that arise in the design procedures for two-channel and M-channel filter banks, a modified version of the Dutta-Vidyasagar algorithm is used. In addition to the optimization-based methods, some iterative methods are introduced. When designing filter banks, the same emphasis is placed on PR and nearly perfect-reconstruction (NPR) filter banks. It has been demonstrated that for most practical applications, the PR property is not needed. By relaxing the PR property, filter banks having better properties can be obtained, such as higher channel selectivity or a shorter filter bank delay. Alternatively, the same overall performance compared to PR filter banks is achievable by using shorter filters in the bank. Many examples are included illustrating the efficiency and flexibility of the proposed design methods.

two-channel filter banks; cosine-modulated filter banks; perfect-reconstruction; nearly perfect-reconstruction; optimization

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