Introduction to algorithms
Multirate Digital Signal Processing
Multirate Digital Signal Processing
Introduction to Linear Optimization
Introduction to Linear Optimization
IEEE Transactions on Signal Processing
Optimal design of FIR filters with the complex Chebyshev errorcriteria
IEEE Transactions on Signal Processing
A polynomial-time algorithm for designing FIR filters withpower-of-two coefficients
IEEE Transactions on Signal Processing
Design of nonuniformly spaced linear-phase FIR filters using mixedinteger linear programming
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Iterative reweighted l1 design of sparse FIR filters
Signal Processing
Design of Sparse Filters for Channel Shortening
Journal of Signal Processing Systems
A class of reconfigurable and low-complexity two-stage Nyquist filters
Signal Processing
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In designing discrete-time filters, the length of the impulse response is often used as an indication of computational cost. In systems where the complexity is dominated by arithmetic operations, the number of nonzero coefficients in the impulse response may be a more appropriate metric to consider instead, and computational savings are realized by omitting arithmetic operations associated with zero-valued coefficients. This metric is particularly relevant to the design of sensor arrays, where a set of array weights with many zero-valued entries allows for the elimination of physical array elements, resulting in a reduction of data acquisition and communication costs. However, designing a filter with the fewest number of nonzero coefficients subject to a set of frequency-domain constraints is a computationally difficult optimization problem. This paper describes several approximate polynomial-time algorithms that use linear programming to design filters having a small number of nonzero coefficients, i.e., filters that are sparse. Specifically, we present two approaches that have different computational complexities in terms of the number of required linear programs. The first technique iteratively thins the impulse response of a non-sparse filter until frequency-domain constraints are violated. The second minimizes the 1-norm of the impulse response of the filter, using the resulting design to determine the coefficients that are constrained to zero in a subsequent re-optimization stage. The algorithms are evaluated within the contexts of array design and acoustic equalization.