Chebyshev optimization of sparse FIR filters using linear programming with an application to beamforming

Sparse FIR filter design, where some tap weights are zero, is of interest as a means of reducing the expense or enhancing the performance of a filter, as a result of fewer or more efficiently placed multipliers. We show that for certain classes of filters with moderately wide passbands, it is possible to increase the stopband suppression by up to 20 dB without increasing the number of multipliers, simply by increasing the number of delay elements, zeroing the appropriate taps, and optimizing the other taps using linear programming. Another use for sparse FIR filters is for the case where multipliers have failed. Graceful degradation can be achieved in some types of FIR filters by optimally adjusting the functional elements to compensate for the failed multipliers. This approach can also be used to minimize the peak sidelobe level for beamformers that may have failed elements. For the beamforming cases considered, the peak sidelobe level was decreased by as much as 5 dB.