Matched Z-transform method: Difference between revisions

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This transform doesn't preserve time- or frequency-___domain response (though it does preserve [[BIBO stability|stability]] and [[minimum phase]]), and so is not widely used.<ref>{{Cite book|url=https://books.google.com/books?id=VZ8uabI1pNMC&lpg=PA262&ots=gSD3om4Hy4&pg=PA262|title=Digital Filters and Signal Processing|last=Jackson|first=Leland B.|date=1996|publisher=Springer Science & Business Media|year=|isbn=9780792395591|___location=|pages=262|language=en|quote=although perfectly usable filters can be designed in this way, no special time- or frequency-___domain properties are preserved by this transformation, and it is not widely used.}}</ref><ref name=":0" /> More common methods include the [[bilinear transform]] and [[impulse invariance]] methods.<ref name=":4" /> MZT does provide less high frequency response error than the BLT, however, making it easier to correct by adding additional zeros, which is called the MZTi (for "improved").<ref>{{Cite journal|last=Ojas|first=Chauhan|last2=David|first2=Gunness|date=2007-09-01|title=Optimizing the Magnitude Response of Matched Z-Transform Filters ("MZTi") for Loudspeaker Equalization|url=http://www.aes.org/e-lib/browse.cfm?elib=14198|journal=Audio Engineering Society|language=English|volume=|pages=|archive-url=http://www.khabdha.org/wp-content/uploads/2008/03/optimizing-the-magnitude-response-of-mzt-filters-mzti-2007.pdf|archive-date=2007|via=}}</ref>
 
A specific application of the ''matched Z-transform method'' in the digital control field, is with the [[Ackermann's formula]], which changes the poles of the controllable system; in general from an unstable (or nearby) ___location to a stable ___location.
 
[[File:Chebyshev responses.svg|thumb|350px|Responses of the filter (dashed), and its discrete-time approximation (solid), for nominal cutoff frequency of 1 Hz, sample rate 1/T = 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.]]