Research On Application Of The Optimisation Technique To FIR Filter And Two-Channel Filter Banks

FIR filter and two-channel filter banks are widely used and their optimisation design has received substantial attention recently. Application of the optimisation technique is studied in this paper, which improves some insufficiencies.For FIR filter,my paper presents a new algorithm for the design of peak constrained filter according to an integral square error criterion. It uses a gradient descent algorithm to correct the coefficients of filter iteratively to achieve the optimum result.My paper also improves some insufficiencies of optimisation technique to two-channel filter banks . First, a direct approach to the design of Quadrature Mirror Filter(QMF) banks without using polyphase decomposition is presented. It minimizes the reconstruction error of QMF banks via minishing amplitude distortion,which bases on the free from aliasing and phase distortion. This approach is distinct from many other filter design methods because it is easy. It can as an initialization approach to two-channel QMF banks.Second, the perfect-reconstruction(PR) requirement imposes nonlinear constraint of two-channel PR linear-phase filter banks to be designed. An efficient iterative Lagrange multiplier approach is developed in this paper, which transforms the nonlinear optimization problem to the problem of minmum weighted mean square error. The approach can be used to design equal-length filter banks. Moreover, it is not sensitive to changes in the initial value.Last, lattice coefficients and the frequency response are serious nonlinear in the design of two-channel lattice-struct perfect-reconstruction filter banks. According to the characteristic of Genetic Algorithm that can solve nonlinear problem which difficultly is ravelled out by conventional methods, and some insufficiency of it to design filter,such as large hunting space ,relapse into part-extremum and slow convergence speed. Some suitable improvements are made for Genetic Algorithm. And improved Genetic Algorithm is used to optimise the design of two-channel lattice-struct filter banks in my paper. Design example is given to show that PR filter banks with good filtering performance can be obtained. Nonlinear problem is solved. Probability and speed of overall convergce are enhanced.