Efficient sparse FIR filter design

We consider the problem of designing a sparse FIR filter and show that it can be cast into a problem of determining a sparse solution of a linear system of equations. Previously proposed design algorithms for FIR filter utilize an intelligent search over all possible structures for sparse filter. We propose a new filter design method based on a simpler algorithm for finding a sparse solution of the linear system. Simulation experiments show significant improvements over classical nonsparse methods.