Research And Design Of Low-complexity Linear Phase FIR Multi-frequency Notch Filter

FIR multiple notch filter has many advantages such as linear phase,high precision and good stability,so that it can be widely used in mobile communication,power systems and biomedical fields.However,when the notch performance is required to be high,higher filter order is usually required,which leads to a huge number of operation units and a large amount of hardware resources in the implementation of the FIR notch filter.Therefore,how to solve the contradiction between high performance and high complexity in the process of designing FIR multiple notch filters has become the focus of research.To reduce the computational complexity and hardware implementation complexity,based on the sparse FIR filter design algorithms and common subexpression elimination(CSE)method,two novel algorithms are proposed for the design of low complexity sparse FIR multiple notch filters.The main contents of this thesis include the following aspects:(1)A novel algorithm is proposed for the design of sparse FIR multiple notch filters with tunable notch frequencies.The proposed design procedure can be proceeded as follow:first,a sparse linear phase FIR single notch filter with a notch frequency of 0 is designed as a fixed prototype filter by the sparse algorithm.Second,according to the given notch frequencies set,a tuning procedure is applied to the computed sparse filter to produce the desired linear phase FIR multiple notch filter.When the notch frequencies are varied,the same tuning procedure does not involve any iteration calculation,avoiding designing the filter from scratch,thus directly reducing the computational complexity of the design algorithm.Moreover,this method has the advantage of high sparsity of filter coefficients,which can greatly reduce the number of adders used in hardware,thus improving the operation speed and reducing the hardware cost.The effectiveness of the proposed algorithm is proved by the simulation experiments,and the actual effect of the tunable notch frequencies is analyzed.(2)A novel algorithm is proposed for the design of low complexity sparse FIR multiple notch filters based on sparse FIR filters design algorithm and CSE method.The proposed design procedure can be proceeded as follow:first,a sparse notch benchmark filter that meets design specification is obtained by the sparse filters design algorithm.Then,each quantized filter coefficient is represented in CSD.And the sensitivities of all weight-two subexpressions and isolated nonzero digits of the quantized coefficient set are analyzed.Finally,the filter coefficient set with lower implementation cost is constructed by iteratively admitting subexpressions and isolated nonzero digits according to their sensitivities.The simulation results show that the proposed algorithm can save about 51%of adder compared with other low complexity filter design algorithms,which effectively reduces the implementation complexity and greatly saves the hardware cost.