Improved IIR Low-Pass Smoothers and Differentiators with Tunable Delay

摘要

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