Filter Magnitude and Phase in s plane

Cuthbert Nyack

If a filter has 3 poles in the s plane then a plot of the magnitude of the transfer function over the complex s plane is illustrated by the applet below which shows a portion of the s plane indicated on the applet. The default parameters show the magnitude when the poles correspond to a chebyshev filter. The frequency response is shown by the heavy yellow line which corresponds to the magnitude along the imaginary axis. The heavy black line shows the start of the -ve real axis.

The above plot shows the magnitude in a portion of the left half of the s plane. The filter transfer function is usually derived from a magnitude squared transfer function which has poles in both halves of the s plane. The complete plot is shown below. THe heavy magenta line is the imaginary s axis and the heavy black line is the real s axis.

The corresponding phase plot over a portion of the left half of the s plane is shown below. The heavy black line is the -ve real axis and the heavy magenta line is the phase along the imaginary s axis.

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