Frequency Transformations in Filter Design
- 1 June 1956
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IRE Transactions on Circuit Theory
- Vol. 3 (2) , 140-144
- https://doi.org/10.1109/TCT.1956.1086291
Abstract
The problem of determining the possible functions\omega = \varphi(y), that will transform the amplitude characteristicA (\omega)of a given network to the amplitude characteristicA[\varphi(y)]of another network, is considered. It is shown that the general form of these transformations is given by\omega = \sqrt{F(y^2)}, whereF(y^2)is a positive rational function ofy^2. The network function whose amplitude characteristic isA[\varphi(y)]is determined from the original network and the functionF(y^2). The concept of frequency transformations is used in filter design and network analysis; the Butterworth and Tchebycheff filters result as special forms of such transformations.Keywords
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