Constant-K/M-Derived Digital Filter/Smoothers.
Austin L. Foote, Walter G. Murch · Defense Technical Information Center (DTIC) · 1974
This report develops the theory and equations for linear, first-order, constant coefficient, differential equations to implement digitally low-pass and high-pass filter/smoothers for use in post-test data reduction and analysis. The derivations are based on the theory developed by O. J. Zabel in 1923 for continuous constant-K/M-derived filters. A constant-K/M-derived filter is a lossy passive filter whose transfer function contains significant poles and zeroes in the 5-domain. This is in contrast to widely used forms of active filters such as Butterworth and Chebyschev whose transfer functions contain only significant poles in the 5-domain. A minimum set of linear differential equations requiring no derivatives or integrals of the input function is derived from the corresponding electrical circuit diagram.