ABSTRACT
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 < w < 1, 0 if |w| > 1) and the sgn function (sgn x = 1 if w > 1, 0 if w = 0, − 1 if w < 0) are needed. Elementary analytical methods lead to rational functions, such as 1 1 + ϵ 2 T n 2 ( w ) or 1 1 + w 2 n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072584/300cbf75-7783-4a6f-9796-7cd4d736d320/content/eq2148.tif"/>
