Arithmetically symmetrical digital bandpass and band‐elimination filter design by frequency transformation
Tsuyoshi Takebe, Masakazu Wakabayashi, Kiyoshi Nishikawa · Electronics and Communications in Japan (Part I Communications) · 1983
Abstract In transmission systems of modulated data or picture signals, bandpass filters are required with symmetrical amplitude and delay characteristics around their own center frequencies on an arithmetic frequency scale. In variable attenuation equalizers, etc., band‐elimination filters are required with arithmetically symmetrical stopband amplitude characteristics around the center frequency. This paper proposes frequency transformations to make an analog bandpass filter and a band‐elimination filter (with geometrically symmetrical amplitude characteristics around the center frequencies that are obtained through reactance frequency transformation from analog lowpass filters) into a digital bandpass filter and a band‐elimination filter with arithmetically symmetrical amplitude characteristics. This transformation maps the positive imaginary axis and the negative real axis of analog frequency S to the real axis and the upper half of the unit circle on the z‐plane. the interval on the unit circle of the z‐plane mapping of the positive imaginary axis of the S‐plane is designed to cover the specified frequency region. This is done by controlling the locations of geometrically symmetrical two frequency points around the center frequency of bandpass (band‐elimination) filter by adjusting the parameters of lowpass‐bandpass (band‐elimination) transformation. Some design examples are also shown.