Infinite impulse response filter 3rd order lowpass Matched Z approximation.

Cuthbert Nyack
The sampled "equivalent" of a third order Butterworth filter derived by use of the Matched Z approximation is shown in the applets below. In these applets only the poles of the Butterworth are matched. The Butterworth filter has an upper 3dB frequency of 1rad/s. The first applet shows the filter response on a log-log scale. The vertical scale for amplitude is in dB and is shown in the scrollbar label as dB/Vdiv. Horizontal scale is in rad/s and goes to a maximum of 2xsampling frequency. Only the range up tp ½ of the sampling frequency is important but the rest is included to show the periodicity of the response. Because of the log scale, the higher periods are greatly "compressed". If the /Hdiv is "a" then the horizontal scale goes from a-1 to a3 rad/s. For phase the vertical scale is from -pi to pi/3.

In both applets red shows the sampled filter response, orange shows the analog filter response, green shows the sampled filter phase and cyan shows the analog filter phase. magenta shows the ideal filter response. The applet below shows the response on a linear scale which gives a better view of what happens at low sampling frequencies. In applet below vertical scale is from 0 to 4/3 and horizontal scale is from 0 to 4rad/s.

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COPYRIGHT © 1999 Cuthbert A. Nyack.