Z Transform 6 Zeros Frequency Response.

Cuthbert Nyack
Applet shows the Impulse and Frequency response of a system with complex conjugate zeros at z1 e±jz1f p/180, z2 e±jz2f p/180 and z3 e±jz3f p/180, 6 poles are included at the origin to make the impulse response zero for t < 0.
Vi and Vg changes gain of impulse and frequency response.

eg parameters (1.0, 70.0, 1.0, 105.0, 1.0, 154.0, NA, 0.22, 47, 0.3)
Applet shows a basic low pass configuration with zeros in the stop band. All zeros are on the unit circle, the impulse response is FINITE and SYMMETRIC and the phase is LINEAR. Moving any of the zeros away from the unit circle by changing z1 or z2 results in the impulse response becoming asymmetric and the phase becoming nonlinear

eg parameters (0.25, 47.0, 4.0, 47.0, 1.0, 164.0, NA, 0.06, 62, 0.09)
Applet shows another low pass configuration with zeros in the stop band. In this case there are 2 zeros in the passband, one inside and one outside the unit circle. The product of z1 and z2 = 1.0 and the angular coordinates of both zeros are the same. The impulse response is still symmetric with some -ve values and the phase is still linear.

eg parameters (1.0, 17.0, 4.0, 133.0.0, 0.25, 133.0, NA, 0.19, 375, 0.10)
Applet shows a high pass configuration with 2 zeros in the pass band. The impulse response is still symmetric but the midvalue is large and -ve.

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Copyright 2008 © Cuthbert A. Nyack.