Re: Warping Pole/Zero Plot

Chris Barrett wrote:
I'm converting between to s domain and the z domain by finding the poles and zeros. My plots of the frequency response look correct, but the scaling on the y-axis is not the same. Does any one know how I fix this?


Here are some more details:

What I have is a continuous time transfer function given by

2*w_d
h(s) = ---------------------
s^2 + 2*w_d*s + w_d^2


Where w_d is the angular frequency of the -6 dB roll off. I find the poles and zeros of this solving the quadratic equation for the denominator and the a simple algebraic one for the numerator. I then convert the poles and zeros to the z^-1 domain by using the following equations

p_z = e^(i*T/p_s)
z_z = e^(i*T/z_s)

I use the poles and zeros in the z domain to find the new coefficients. I find a new transfer function from this and plot it. This is improperly scaled function I referred to in the first paragraph.

A couple of corrections:

I'm actually going from the omega-plane to the z-plane where

s = i*omega.

When I find the poles and zeros by solving the quadratic, I am solving it for omega and not s.

My transfer function was suppose to be

w_d^2
h(s) = ---------------------
s^2 + 2*w_d*s + w_d^2
.

Relevant Pages

  • Re: Poles an Zeros
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    (sci.electronics.basics)
  • Warping Pole/Zero Plot
    ... My plots of the frequency response look correct, but the scaling on the y-axis is not the same. ... I find the poles and zeros of this solving the quadratic equation for the denominator and the a simple algebraic one for the numerator. ...
    (comp.dsp)
  • Re: filter with arbitrary and variable rolloff
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  • Re: Value of coupling caps
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    (rec.audio.tubes)
  • Re: Bandpass system identification using IIRs (audio)
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