A resonance filter is a specific second-order digital system designed to attenuate all frequencies except at and around a given center frequency (f.), in Hz. The transfer function of a resonance filter is: (1 – r) (1 – rz-2) 1- 2r cos(w.T)z-1 + r²z-2' H(2) = where we= 2n fe, nd r is a parameter that controls the resonance bandwidth. Show that, for any given resomance frequency wcand any value of the parameter r, the amplitude response of the filter equals unity at o = oc, i.e. show that |H(oc)| = 1.
A resonance filter is a specific second-order digital system designed to attenuate all frequencies except at and around a given center frequency (f.), in Hz. The transfer function of a resonance filter is: (1 – r) (1 – rz-2) 1- 2r cos(w.T)z-1 + r²z-2' H(2) = where we= 2n fe, nd r is a parameter that controls the resonance bandwidth. Show that, for any given resomance frequency wcand any value of the parameter r, the amplitude response of the filter equals unity at o = oc, i.e. show that |H(oc)| = 1.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Transcribed Image Text:A resonance filter is a specific second-order digital system designed to attenuate all frequencies
except at and around a given center frequency (fe), in Hz. The transfer function of a resonance
filter is:
(1 – r) (1 – rz-2)
1- 2r cos(w.T)z-1+r2z-2'
H(z) =
%3D
where w.= 27fe, nd r is a parameter that controls the resonance bandwidth.
Show that, for any given resonance frequency wcand any value of the parameter r, the amplitude
response of the filter equals unity at o = oc, i.e. show that |H(oc)| = 1.
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