Improved IIR Low-Pass Smoothers and Differentiators with Tunable Delay

TL;DR

This paper introduces improved IIR low-pass smoothers and differentiators with tunable delay, achieved through orthogonal polynomial regression, enabling customizable phase response for applications like optical flow and target detection.

Contribution

It presents a novel derivation of IIR filters with adjustable delay and phase response using orthogonal polynomial regression and modified exponential weighting functions.

Findings

Enhanced filter response with shape modification of weighting function

Tunable delay in pass band and zero gain at Nyquist frequency

Successful application in optical flow and target detection

Abstract

Regression analysis using orthogonal polynomials in the time domain is used to derive closed-form expressions for causal and non-causal filters with an infinite impulse response (IIR) and a maximally-flat magnitude and delay response. The phase response of the resulting low-order smoothers and differentiators, with low-pass characteristics, may be tuned to yield the desired delay in the pass band or for zero gain at the Nyquist frequency. The filter response is improved when the shape of the exponential weighting function is modified and discrete associated Laguerre polynomials are used in the analysis. As an illustrative example, the derivative filters are used to generate an optical-flow field and to detect moving ground targets, in real video data collected from an airborne platform with an electro-optic sensor.