The Design Of Arbitrary-length Linear-phase Cosine-modulated Filter Bank

Multirate digital signal processing techniques have been studied by engineers for about forty years. The theory of multirate digital signal processing gradually comes to mature and the applications of multirate digital signal processing emerge endlessly, especially in the field of designing multirate filter banks, there have been various filter banks which can reconstruct the signal perfectly. Linear phase cosine modulated filter bank is one of the filter banks with perfect reconstruction, its all analysis and synthesis filters can be obtained by modulating the coefficient values of one prototype filter and it can be designed and implemented efficiently. For these advantages, linear phase cosine modulated filter bank is used in many applications, such as audio/video coding, mobile communication, soft-defined radio and radar, at the same time, linear phase cosine modulated filter bank has been extensively studied.Up to now, the length of the prototype filter of many linear phase cosine modulatedfilter banks is restricted. A variety of approaches are available for the design of the prototype filter. Most of the approaches use standard constrained or unconstrained optimization techniques to obtain the design, which tend to be computationally expensive, especially when the number of filter coefficients is high. Moreover, the standard optimization techniques are usually sensitive to changes in the initial values. To obtain satisfactory design results, a large set of designs with different initial values may be required.In this paper, an arbitrary length linear phase cosine modulated filter bank is introduced and the perfect reconstruction criteria for this filter bank is established. An efficient approach is developed to design arbitrary length linear phase cosine modulated filter bank. The design problem is first formulated as a quadratic constrained least squares optimization problem, and then use an efficient iterative Lagrange multiplier approach to solve this optimization problem. The perfect reconstruction criteria for arbitrary length linear phase cosine modulated filter bank can be satisfied by four modes, every mode has its own characteristics, so the corresponding design is different. In this paper, several design examples introduce in detail how to use the method proposed by this paper to design the prototype filter under different modes of the perfect reconstruction criteria.The design examples are presented to demonstrate the effectiveness of the proposed algorithm. Compared with the non-linear optimal design, the method proposed by this paper is simple, efficient and useful.