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.
Regression analysis using orthogonal polynomials in the time domain is used to derive a digital filter with an infinite impulse response that satisfies maximally flat design constraints near dc. The low-frequency phase, and high-frequency gain, may be adjusted for lead or lag compensation of plant dynamics.Simulated design examples are used to show how the compensating filter may be intuitively tuned for the desired closed-loop response. It is shown that the second-order instantiation of the compensating filter reduces to a proportional-differential plus filter controller, with improved noise attenuation; closed-form expressions for the filter coefficients, as a function of two design parameters, are provided.Index Terms-Control design, digital control, digital filter design, infinite impulse response (IIR) filters, Savitzky-Golay (S-G) filtering.
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