Finite Precision Design of Linear-Phase FIR Filters

Abstract

The fir (finite impulse response) filter is an essential tool for a large number of applications in communication. In this paper we consider the design of linear‐phase fir digital filters with finitely precise coefficients. Coefficient inaccuracy is known to degrade the frequency response of band‐select fir filters, especially in the stopband region. We derive a bound on the attainable stopband attenuation, and we also develop techniques for designing fir filters with finitely precise coefficients. Mixed‐integer programming algorithms are presented to select finitely precise coefficients for a filter that best approximates an arbitrary magnitude characteristic in the minimax sense. Our method generates a number of possible solutions including that of simple rounding or truncation and then selects the best finitely precise coefficients from this set. In this way, significant improvement in the filter performance is gained over methods that simply round or truncate the infinitely precise coefficients. We also show how integer programming can be used to design filters with powers of two coefficients. Such filters are easier to mechanize since they do not require multipliers.

Applications of simulated annealing for the design of special digital filters

“….. ,ad, with (2) In (1), B is an integer representing the maximum number of shifts that can be perfonned on the filter input signal. It is seen that values of Xi are within the interval [ -1, 1] and they are not distributed unifonnly.…”

Low-precision Logarithmic Number Systems

“…Smaller word sizes can reduce the memory footprint of data, and the complexity of arithmetic for a variety of number systems [9,14,17,33], which will have a significant impact on the ability to deploy systems in resource constrained embedded devices deployed on the edge of networks. Further, fixed-point number systems with very short word lengths have been proposed in the literature for a variety of signal processing applications [2,24], while shorter floating-and fixedpoint numbers have also been used for neural networks [8,18,19,39,43,44].…”

Low precision logarithmic number systems: Beyond base-2

“…Smaller word sizes can reduce the memory footprint of data, and the complexity of arithmetic for a variety of number systems [9,10,11,12,13,14] which will have a significant impact on the ability to deploy systems in resource constrained embedded devices deployed on the edge of networks. Further fixed point number systems with very short word lengths have been proposed in the literature for a variety of signal processing applications [15,4] while shorter floating and fixed point numbers have also been used for neural networks [16,17,18].…”