Research On The Theory Of Low Complexity Digital Filter Design

With the development of digital signal processing technology, digital filters have been widely used. Finite impulse response (FIR) digital filters have attracted much attention due to its strictly linear phase property and stability. However, the most disadvantage of the FIR digital filter is its high order for implementation when the design specification is high. As a result, how to design the low complexity digital filter is an important issue, which deserves to be carefully researched.This paper focuses on the theory of the low complexity digital filters, mainly concerns with the two newly developed theory of low complexity digital filter:reconfigurable filter and sparse filter. The main contributions of this paper including:1. A second-order cone programming (SOCP) based algorithm is proposed for the design of reconfigurable frequency response masking (FRM) filters. In previous methods for the design of reconfigurable FRM filters, all the subfilters were designed separately which makes the solutions suboptimal. We propose an improved method for the design of reconfigurable frequency response filters, which takes all desired designing modes into consideration. The proposed method takes two steps:firstly an initial solution is obtained by separately designing the subfilters, and then the initial solution is updated by iteratively solving a SOCP problem. Simulation results demonstrate that the method offers significantly lower approximation errors compared to the conventional design method.2. A reweighted L1 optimization based algorithm is proposed for the design of sparse coefficient decimation filter. In order to reduce the multipliers of the coefficient decimation filter, we investigate the sparse design of it. The proposed method transforms the sparse design of coefficient decimation filter into a reweighted L1 optimization problem. At each step of the method, a reweighted L1 optimization problem is solved subject to the filter design specifications. Then, the nonzero-valued coefficient with the smallest absolute value is chose and sets to 0 at the next step. With the iteration of the reweighted L1 optimization, the sparsity of the filter is successively increased, until no sparser solution satisfiing the filter design specifications exists. Simulation results demonstrate that the proposed method could effectively reduce the multipliers of the coefficient decimation filter.3. A binary particle swarm optimization (BPSO) based algorithm is proposed for the design of sparse FIR filter. Due to the highly nonconvex property of the sparse FIR filter design subject to the prescribed design specifications, we employ the BPSO algorithm. The algorithm iteratively uses BPSO to determine the sparse pattern of the FIR filter with a fixed sparsity of the filter coefficients at each step. Once the global best particle produce a design result satisfying the prescribed design specifications, the sparsity of the FIR filter is added by one and then move to the next step of the algorithm. The procedure of the algorithm terminates until no improvement of the sparsity could be achieved. Simulation results demonstrate that the proposed method could achieve sparser design results than other existing algorithm.4. A simulated annealing based algorithm is proposed for the design of low group delay sparse filter. Due to the high group delay of the sparse filter when compared to the non-sparse filter with the same design specifications, a simulated annealing based algorithm is proposed. The proposed method transforms the sparse design of low group delay filter into a combinatorial optimization problem, and uses the simulated annealing algorithm to solve it. At each step of the method the sparsity of the low group delay filter is fixed, simulated annealing algorithm is used for finding the set of the positions of the zero filter coefficients that satisfies the design specifications. Once the specifications have been satisfied, the sparsity of the filter is added by one and then the algorithm moves to the next step until no sparser solution exists. Simulation results demonstrate that the proposed method could achieve sparser result than conventional methods.