Research And Design Of A Sparse FIR Cosine Modulation Filter Bank With Approximately Complete Reconstruction

In the multi-rate signal processing system,cosine-modulated filter bank(CMFB)is one of the most important basic modules.Its design principle is simple and easy to realize,and it is widely used in mobile communication,image processing,radar and other fields.As the large number of tap coefficients required by the high-precision non-sparse cosine-modulated filter banks,the operation cost of add and multiplier is huge in hardware design,and the system delay and implementation complexity are high.In order to solve this problem,this paper presents two design methods of sparse FIR cosine-modulated filter banks satisfying the nearly perfect reconstruction property.By reducing the number of non-zero coefficients of prototype filter,the cost of hardware implementation is reduced effectively.The main work of this paper is as follows:(1)A design method of sparse FIR cosine-modulated filter banks based on the Hopfield neural network(HNN)has been proposed.Firstly,according to the Hopfield neural network structure and the design requirements of cosine-modulated filter banks,the Lyapunov energy function is bonded to the error function of cosine-modulated filter banks.Then,the non-zero coefficient position of prototype filter is obtained by using the orthogonal matching pursuit(OMP)algorithm,and the corresponding coefficient set is input into the Hopfield neural network for training.When the energy function of the Hopfield neural network reaches the convergence state,that is,the error function of the prototype filter is minimized.By filling the output voltage of the Hopfield neural network with zero according to the non-zero coefficient position,the optimal sparse prototype filter coefficient is obtained.Finally,the sparse cosine-modulated filter bank is obtained by cosine modulation.From the comparative analysis of the simulation results,it shows that this method can design a sparse cosine-modulated filter banks which can satisfy the nearly perfect reconstruction property.(2)A design method of sparse FIR cosine-modulated filter banks based on the quantum particle swarm optimization algorithm has been proposed.First,the non-zero coefficient position of prototype filter is obtained by using the orthogonal matching pursuit algorithm.Then,the non-zero coefficients of the prototype filter corresponding to the position set are optimized by the quantum particle swarm optimization algorithm to minimize the error value of the objective function.Finally,the sparse cosine-modulated filter bank is obtained by cosine modulation.Through the comparative analysis of simulation results,it can be seen that the cosine-modulated filter banks designed by this method has good sparsity while satisfying the nearly perfect reconstruction property.