IIR Filters for Postprocessing Noisy Test Data

A little-known parametric form of an infinite impulse response (IIR) filter has been found to be useful in digital postprocessing of noisy test signals. The filter equation is:

y(n) = α[x(n) + x(n – 1)] + γy(n – 1),

n) and y(n) are the input and output, respectively, during the nth sampling period. The parameters are given by

γ = cos θ_c/(1 + sin θ_c) and α = (1 – γ)/2,

where θ ≡ 2πf/f_s; θc ≡ 2πf_c/f_s; and f, f_s, and f_c are frequencies. This parametric form simplifies postprocessing and analysis of the data by making it easy to tune the filter response through selection of the low-pass cutoff frequency, f_c. Whereas parameters in other forms of IIR filters are restricted to discrete values, the parameters in this form can be selected from nearly continuous ranges. The filter response in this form is inherently stable over the entire digital frequency range from zero to the Nyquist frequency (half of the sampling frequency, f_s). Although the stability is robust, it deteriorates with a decrease in the number of bits used to represent coefficients and filter states.

This work was done by Jan A. Zysko and Christopher M. Amis of Kennedy Space Center and John E. Lane of Dynacs, Inc. For further information, access the Technical Support Package (TSP) free on-line at www.nasatech.com/tsp under the Information Sciences category. KSC-12218

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