Design Of Cosine Modulated Filter Banks With Perfect Reconstruction

Multirate filter banks have various important applications in communications, transmultiplexing, subband coding of speech and images, radar, adaptive filter, denoising, system indentification and many other fields. There are many advantages of the filter banks such as reduced computational complexity, reduced transmission rate, reduced storage requirement. In multirate digital filter banks system, the cosine modulated filter banks have received widespread attention and are the most frequently used filter banks at present. They can achieve perfect reconstruction by optimizing the prototype filter and all analysis and synthesis filters are obtained from the prototype filter. Cosine modulated filter banks are well known for their low design and implementation cost.In this paper, the design of the cosine modulated filter banks with perfect reconstruction are studied in details with emphasis on the design of biorthogonal cosine modulated filter banks and oversampled cosine modulated filter banks. The system delay in orthogonal cosine modulated filter banks is equal to the order of the prototype filters. Consequently, filter banks with long filters have long system delay, which are highly undesirable in applications such as communication signal processing, real-time signal processing. Biorthogonal cosine modulated filter banks that can provide variable system delay is a good choice for such applications. An efficient iterative Lagrange multiplier approach for biorthogonal cosine modulated filter banks is proposed. The constraints of oversampled cosine modulated filter banks with perfect reconstruction are deduced in this paper and then we propose an iterative method for designing the prototype filter.The general nonlinear optimization techniques are usually employed, which, in general, are complicated and time consuming. Compared with standard nonlinear techniques, the design approach we proposed in this paper has low design cost, high design efficiency and simple structure. In order to verify the effectiveness of this algorithm, several computer simulations have been shown.Finally, we sum up above work and give a forecast of further research.