World Library  
Flag as Inappropriate
Email this Article

Matched Z-transform method

Article Id: WHEBN0030782834
Reproduction Date:

Title: Matched Z-transform method  
Author: World Heritage Encyclopedia
Language: English
Subject: Impulse invariance, Bilinear transform, Hexagonal sampling, Nyquist rate, Digital image processing
Collection: Control Theory, Digital Signal Processing, Filter Theory
Publisher: World Heritage Encyclopedia

Matched Z-transform method

The s-plane poles and zeros of a 5th-order Chebyshev type II lowpass filter to be approximated as a discrete-time filter
The z-plane poles and zeros of the discrete-time Chebyshev filter, as mapped into the z-plane using the matched Z-transform method with T = 0.1 second. The labeled frequency points and band-edge dotted lines have also been mapped through the function exp(sT), to show how frequencies along the axis in the s-plane map onto the unit circle in the z-plane.

The matched Z-transform method, also called the pole–zero mapping[1][2] or pole–zero matching method,[3] is a technique for converting a continuous-time filter design to a discrete-time filter (digital filter) design.

The method works by mapping all poles and zeros of the s-plane design to z-plane locations z = exp(sT), for a sample interval T.[4]

Alternative methods include the bilinear transform and impulse invariance methods.

Responses of the filter (dashed), and its discrete-time approximation (solid), for nominal cutoff frequency of 1 Hz, sample rate 10 Hz. The discrete-time filter does not reproduce the Chebyshev equiripple property in the stopband due to the interference from cyclic copies of the response.


  1. ^ Won Young Yang (2009). Signals and Systems with MATLAB. Springer. p. 292.  
  2. ^ Bong Wie (1998). Space vehicle dynamics and control. AIAA. p. 151.  
  3. ^ Arthur G. O. Mutambara (1999). Design and analysis of control systems. CRC Press. p. 652.  
  4. ^ S. V. Narasimhan and S. Veena (2005). Signal processing: principles and implementation. Alpha Science Int'l Ltd. p. 260.  
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.