| The two-channel Quadrature Mirror Filter Bank(QMFB)has research significance and application value in the field of audio/video processing,image compression,wavelet analysis,radar signal processing.The two-channel QMFB based on finite impulse response(FIR)filters can achieve linear phase and no aliasing distortion.For the design of a two-channel QMFB,currently existing methods are mainly proposed to optimize frequency domain performance,and there is still room for improvement in terms of implementation complexity.This thesis is focused on the problem of designing and optimizing a two-channel QMFB with sparse coefficients.The research work includes:First,an optimization algorithm based on Lp-norm minimization for designing a two-channel QMFB with sparse coefficients is proposed.The algorithm generally includes two steps: initially,the coefficients of a prototype FIR filter are optimizing by trust region-iterative gradient searching(TRIGS)algorithm,and then the coefficients are sparsely transformed based on the iterative optimization of Lp-norm minimization.The first step of the proposed algorithm transforms the non-convex optimization design of the coefficients into a convex optimization problem oriented to the variation of the coefficients with the help of the Taylor approximation.The purpose of this step is improving the frequency domain performance of the two-channel QMFB.The second step of the proposed algorithm focuses on solving L0-norm of the coefficients.This step minimizes the variable coefficients by different p-norm values in order to make sparse transformation and harvest as many zero-valued coefficients as possible.Data of simulation show that,compared with existing methods,the proposed algorithm can improve the sparsity of the coefficients while reducing the stop-band error and distortion error.Additionally,the algorithms under different p-norm values are all effective.Second,an optimization algorithm based on matrix decomposition to designing a two-channel QMFB with sparse coefficients is proposed.The algorithm mainly includes two parts.To begin with,a new set of coefficients is obtained through reasonable matrix decomposition to achieve preliminary sparseness.Then,further sparse transformation and optimization for each part of the variable coefficients after decomposition are accomplished by Lp-norm minimization.The results of different simulation examples show that several 0-value and 1-value coefficients can be preliminarily obtained through matrix decomposition,which reduces the implementation complexity of the corresponding two-channel QMFB.What’s more,the proposed algorithm combined with Lp-norm minimization and sparse transformation of new variable coefficient sets can help to further improve the sparsity.Third,based on the algorithms proposed above,the prototype FIR filter of two-channel QMFB is implemented based matrix decomposition in FPGA hardware.To start with,the model building and simulation are completed on the MATLAB Simulink for two examples,and the fixed-point analysis of coefficients is carried out.The simulation output results verify that the special FIR structure under the proposed algorithm is reasonable and feasible,and it can lower implementation complexity of the corresponding two-channel QMFB by reducing the use of multipliers and adders.The data of simulation also shows that the fixed-point coefficient will affect the performance in frequency domain.Then,the co-simulation based on Quartus Ⅱ and Modelsim for each example is accomplished.The output waveform results and performance indicators after calculated are in line with the theoretical analysis.Finally,the FPGA onboard implementation and testing were completed for different examples.The actual export data shows that the special structure based on the proposed algorithm can be effectively implemented in FPGA.Furthermore,compared with the existing three traditional methods,the proposed method can cost fewer hardware resources and reduce power dissipation. |
