Analysis and Synthesis of Delay Line Periodic Filters
- 1 June 1957
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IRE Transactions on Circuit Theory
- Vol. 4 (2) , 41-53
- https://doi.org/10.1109/TCT.1957.1086353
Abstract
A periodic filter has a frequency characteristic which is periodic. Such filters can be constructed using delay lines where the delay of each line is the reciprocal of the basic frequency period. The network function of the periodic filter is characterized by the presence of the factors of the forme^{np\tau}, wherenis a positive or negative integer,\tauis the delay of each delay line, andpis the complex frequency variable. Analysis and synthesis are simplified by use of theztransform which has been used with much success in the study of sampled data systems. A transformation of the filter network function is made by substitutingzfore^{p\tau}. This substitution transforms the imaginary axis of thepplane into the central unit circle in thezplane. The properties of the periodic filter are now characterized by the poles and zeros of thez-plane transform. A rational method is presented for synthesizing anyz-plane transform expressed as a rational fraction. Finally, thez-transform concept is used to analyze the behavior of periodic filters with pulsed inputs.Keywords
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