Rational Approximation of the Step, Filter, and Impulse Functions
Yasuhiko Ikebe, Marek A. Kowalski, Frank Stenger · 2020
Modern design of electronic filters, such as low-pass, high-pass and bandpass filters includes the construction of a rational function which satisfies the desired specifications for cut-off frequencies, pass-band gain, transition band-width, and stop–band attenuation [ 1 , Chapter 13 ]. Thus rational function approximations to the χ *-function ( χ* ( w ) = 1 if −1 1) and the sgn function (sgn x = 1 if w > 1, 0 if w = 0, − 1 if w