Extrapolated Impulse Response Technology Based Low Complexity Quadrature Mirror Two-channel Filter Bank

The two-channel finite impulse response quadrature mirror filter bank(2c-FIR-QMFB)is widely used in speech codec,wavelet bases design,and bio-medical signal processing.With the development of the application of 2c-FIR-QMFB,the design of a 2c-FIR-QMFB is becoming more and more important both theoretically and practically.The existing 2c-FIR-QMFB design methods are generally very complex and/or still have room for improvement in the frequency domain performance.Additionally,in some application scenarios,2c-FIR-QMFB is required to have high frequency domain performance.The order of the sub-filter of the corresponding filter bank should be very large.This will result in higher hardware implementation complexity and more multiplication and addition calculations per unit time.This thesis is focused on the two aspects of the 2c-FIR-QMFB design: How to improve the algorithm in terms of the frequency domain design error and how to reduce the implementation complexity.The main research work of this thesis includes:1)Based on the convex optimization theory,two algorithms are proposed to optimize the coefficients of the 2c-FIR-QMFB: iterative gradient searching(IGS)algorithm and iterative linear dimensionality reduction(ILDR)algorithm.Because the two proposed algorithms can both solve the traditional weighted muti-objective optimization problem(in the 2c-FIR-QMFB design)and the single-objective optimization problem(in the 2c-FIR-QMFB design)with constraints,the two algorithms are flexible in implementation.Particularly,for the latter case,the 2c-FIR-QMFB design becomes more convenient.Simulation results show that the IGS and ILDR algorithms have smaller frequency domain design errors and higher search efficiency than previously existing methods.2)It is proposed to design a 2c-FIR-QMFB by using the extrapolated impulse response(EIR)technique.The(direct and efficient)multi-phase structures of the EIR based 2c-FIR-QMFB are correspondingly derived.The hardware implementation complexity of the proposed EIR based 2cFIR-QMFB is obviously lower especially for a 2c-FIR-QMFB of higher sub-filter order.Further,the multiplication/addition computation complexity per unit time is reduced.Thus,this EIR based structure is of certain practical value.Additionally,a new coefficient optimization algorithm for this EIR based structure is proposed,namely LDR-IGS.This optimization algorithm improves the frequency domain performance of the EIR based 2c-FIR-QMFB.3)The EIR based multi-phase structure is simulated and analyzed in the FPGA simulation platform.First,the EIR based multi-phase structure is verified in the MATLAB/Simulink platform.Second,the EIR based multi-phase structure is simulated in Quartus II platform.Some specific design tactics and the design procedure are proposed.Finally,MATLAB and Modelsim are utilized to simulate the performance of the EIR-2c-FIR-QMFB.The simulation results reveal that the hardware implementation complexity of the EIR based 2c-FIR-QMFB is reduced compared to the traditional 2c-FIR-QMFB.However,the quantization error of the former 2c-FIR-QMFB is comparatively large.Additionally,the performance of the former 2c-FIR-QMFB in the max system clock speed is not good.The reasons for this experimental phenomenon are investigated.And,some suggestions for improving the performance are proposed.