FIR Filter Realization Under the Trade-Off Between Implementation Complexity and Computation Rate

Abstract

We propose a flexible finite impulse response (FIR) filter structure which can avail the benefits of trade-off between computation units and clock rate. For designing such flexible FIR filter, we first present two supporting structures viz., Structure I and Structure II. Structure I realizes the FIR filter via single multiplier, single adder, and $N$ delays, where all units operate at the rate of $Nf_{in}$ (i.e., high clock rate), and $N$ and $f_{\mathrm{i}n}$ denote the order of FIR filter and input sampling frequency, respectively, whereas Structure II implements the FIR filter using NM multipliers, M N - M2 adders, and M N - M2 delays in the filter unit with clock rate $\displaystyle \frac{f_{in}}{M}$ (i.e., computationally low-speed realization), and $M-1$ adders and delays at the output unit operate at $f_{in}$, where 2 $\leq M \leq N$ and $M$ denotes the upsampler/downsampler. Then, we propose Structure III via Structures I & II, which provides the flexible realization of FIR filters under the trade-off between computational units and clock rate. We also analyze the performance of these structures in terms of number of multipliers $(C_{M})$, number of adders $(C_{A})$, number of delays $(C_{D})$, and operating frequency $(F_{opt})$ with the help of numerical example in comparison of the direct form FIR filter.