Algorithms for Low Power FIR Filter Realization Using
Differential Coefficients, N. Sankarayya, K. Roy · 1997
A6st~act- We present a Set of new algorithms for lowpower realization of FIR filters which use various orders of differences between coefficients for computing the convolution with the input data. Also the results of computations are stored and reused, thus requiring more storage and storage accesses. These techniques result in a reduction in the computations necessary per convolution as compared to directly using the coefficients. It is shown analytically that this computational reduction at the price of more storage can result in a reduction in net energy dissipated. Realieation of some example FIR filters using these algorithms is analyzed. I. Introduction HE recent proliferation of portable battery-powered T gadgets that make extensive use of Digital Signal Processing (DSP) and demand an ever improving performance, like cellular phones, laptop computers, etc. has made lowpower-high-performance DSP increasingly important. One of the most basic operations performed in DSP applications is Finite Impulse Response (FIR) filterin . An N-tap FIR filter performs the following convolution 771: N- 1 k=O The ck's are called the coefficients of the filter, Xj and % are the j-th component of the input and output sequences respectively. Implementation methods for FIR filters can vary widely from one that uses dedicated hardware multipliers and adders to one that uses code which is executed by a general purpose processor and its ancillary units. A combination of hardware and software that allows sharing of multi-purpose hardware units (like adders and multipliers), without using a full-fledged processor can also be used. In all these implementations the basic FIR filtering algorithm called the multiply and accumulate sequence, remains the same: for any j, each product term CkXj-k in Eqn. (1) is computed, and they are added up to obtain E;.. Consequently, in all these implementations, the nature and number of multiplications performed and the power dissipated therein remain essentially the same.