Some Comparisons Between FIR and IIR Digital Filters

Abstract

The purpose of this paper is to make comparisons between optimum, linear phase, finite impulse response (FIR) digital filters and infinite impulse response (IIR) digital filters which meet equivalent frequency domain specifications. The basis of comparison is, for the most part, the number of multiplications per sample required in the usual realizations of these filters–‐i.e., the cascade form for IIR filters, and the direct form for FIR filters. Comparisons are also made between group‐delay equalized filters and linear phase FIR filters. Considerations dealing with finite word‐length effects are discussed for both these filter types. A set of design charts is also presented for determining the minimum filter order required to meet given low‐pass filter specifications for both digital and analog filters.

Effects of Quantization in Systolic 2D IIR Beam Filters on UWB Wireless Communications

“…The reduction of the number of antennas as well the reduction in computational complexity depends on the bandwidth and selectivity of the beamformer. In general, 2D FIR filters have 10-100 times the computational complexity of 2D IIR filters of similar selectivity levels [11].…”

“…The output of the ADC is assumed to be at quantizer Q 1 [ ] at a smaller precision of (W b , D b ), which implies a sign extension before being submitted to the adder that computes the output at quantizer Q 5 [ ]. The output port quantizer Q 11 [ ] is also fixed at the same precision of Q 6 …”

“…For each case, the internal registers were chosen to be much larger than the ADC precision by choosing A b = 8, B b = 4 according to Table 1, so that the ADC quantization noise dominated the measured performance. For example, for the case 11 [ ] possess the largest register sizes in the systolic array according to Table 1, with each register being 16 bits long and the binary point at bit position 11 (i.e., 11 bits of fractional precision. )…”

Optimum design of group delay equalizers

“…Various design techniques have been proposed with the objective of producing selective digital networks that exhibit approximately linear phase in the frequency band of interest [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. A widely applied technique is phase or delay equalization, by cascading a selective IIR elliptic filter to an equalizer, generally composed by first-and second-order allpass filters [3,4].…”

On the input output behavior of the Hilbert transform

“…There are also some relations to the low pass [5] 161. Let S be an arbitrary linear time invariant system with 00…”