Sparse Finite Impulse Response Filters Research Articles

Iterative Greedy LMI for Sparse Control

In this letter, we propose a novel method to find matrices that satisfy sparsity and LMI (linear matrix inequality) constraints at the same time. This problem appears in sparse control design such as sparse representation of the state feedback gain, sparse graph representation with fastest mixing, and sparse FIR (finite impulse response) filter design, to name a few. We propose an efficient algorithm for the solution based on Dykstra's projection algorithm. We then prove a convergence theorem of the proposed algorithm, and show some control examples to illustrate merits and demerits of the proposed method.

Design of Sparse FIR Filters With Reduced Effective Length

In this paper, an exchange algorithm is proposed to design sparse linear phase finite impulse response (FIR) filters with reduced effective length. The sparse FIR filter design problem is formally an ${l} _{0}$ -norm minimization problem. This original design problem is re-formulated by encoding the filter coefficients using a binary encoding vector, which represents the locations of the zero and non-zero filter coefficients. An iterative 0-1 exchange process with proper direction control is proposed to propel the minimax approximation error toward the specified upper bound of error for sparsity maximization. The effective length is optimized with a lower priority than sparsity in the proposed algorithm. Simulation results show that the proposed algorithm is superior to the existing algorithms in terms of both sparsity and/or effective length in most cases.

A Novel Design of Sparse FIR Multiple Notch Filters with Tunable Notch Frequencies

We focus on the design of finite impulse response (FIR) multiple notch filters. To reduce the computational complexity and hardware implementation complexity, a novel algorithm is developed based on the mixture of the tuning of notch frequencies and the sparsity of filter coefficients. The proposed design procedure can be carried out as follow: first, since sparse FIR filters have lower implementation complexity than full filters, a sparse linear phase FIR single notch filter with the given rejection bandwidth and passband attenuation is designed. Second, a tuning procedure is applied to the computed sparse filter to produce the desired sparse linear phase FIR multiple notch filter. When the notch frequencies are varied, the same tuning procedure can be employed to render the new multiple notch filter instead of designing the filter from scratch. The effectiveness of the proposed algorithm is demonstrated through three design examples.

Sparse FIR Filter Design Based on Simulated Annealing Algorithm

Design of sparse finite impulse response (FIR) filter is of great importance to reduce the implementation cost. However, design of sparse FIR filter under the prescribed constraints is ...

Autocorrelation noise removal for optical coherence tomography by sparse filter design

We present a reconstruction method to eliminate the autocorrelation noise (ACN) in optical coherence tomography (OCT). In this method, the optical fields scattered from the sample features are regarded as the response of a sparse finite impulse response (FIR) filter. Then the OCT reconstruction is formulated as one of identifying the parameters of a sparse FIR filter, which are obtained via an [script-l](1) optimization with soft thresholding. The experimental results show that the proposed method can obtain OCT reconstruction results with effective attenuation of ACN.