The IUP Journal of Telecommunications
Sparse FIR Filter Design Using Orthogonal Matching Pursuit

Article Details
Pub. Date : May, 2019
Product Name : The IUP Journal of Telecommunications
Product Type : Article
Product Code : IJTC31905
Author Name : Priyanka Dalal and Ritu Boora
Availability : YES
Subject/Domain : Science & Technology
Download Format : PDF Format
No. of Pages : 09



Digital filters are used in a wide variety of signal processing applications. To improve the implementation efficiency of a digital filter, design of filters with sparse impulse response is a good solution and is currently a hot research area. Compressive sensing is an emerging signal processing technique for data acquisition, wherein a sparse signal is recovered from a highly incomplete set of measurements. The paper utilizes one of the well-known compressive sensing recovery algorithms, i.e., Orthogonal Matching Pursuit (OMP), to design a Finite Impulse Response (FIR) digital filter with sparse impulse response. Numerical example is taken to demonstrate the utility of the above-mentioned algorithm. The results demonstrate that at the cost of losing some optimality, one can design reasonably sparse FIR filters using OMP.


Digital filters are used nowadays in a wide variety of applications because of numerous reasons like storage capability, easy design, adaptability and many more. They play a major role in communication networks, consumer electronics, speech processing and image processing. Among digital filters, the Finite Impulse Response (FIR) filter has got linear phase response and is always stable, and hence plays an important role (Saramaki, 1993).

The traditional FIR filter designing methods like the algorithm of McClellan et al. (1973) aimed to obtain an optimum filter, but the disadvantage was that they require a large number of multipliers while implementing. Thus, the implementation efficiency was seldom taken into account by the traditional method. Since then, researchers have been working to develop efficient algorithms to enhance the implementation efficiency. The coefficients of an FIR filter can also be represented as the sum of Signed Power-of-Two (SPT) terms. By doing so, the multipliers for the filter coefficient can simply be replaced by adders and shifters. Traferro et al. (1999), Yong et al. (1999) and Izydorczyk and Cionaka (2008) proposed algorithms which minimized adders for filters represented by SPT coefficients. Xu et al. (2007) and Mahesh and Vinod (2008) proposed methods that further reduce the number of adders by Common Subexpression Elimination (CSE).


Sparse FIR filter, Sparsity, Compressed sensing, Optimality, Orthogonal Matching Pursuit (OMP)