second order Butterworth filter

Can any one tell me how to plot the frequency response for the following digital second order Butterworth filter using MATLAB.

(1+2*z^-1+z^-2)/(10.2358-9.6464z^-1+3.4106).

This should be a low pass filter with cutoff at 1KHz. You can plot up to 8 KHz so that we can show the aliasing also

[Walter Roberson]

Are you sure you want the denominator to have two coefficients that are independent of z? Are you sure that one of the two should not be followed by z^-2 ?

Answer 1

[Star Strider]

I would address Walter’s concerns about the missing z term, then convert it to a transfer function (vector) representation, and use the freqz function to create the Bode plot.

I don’t know what you mean by ‘show the aliasing also’ since to the best of my knowledge, you can only filter up to the Nyquist frequency with a properly-designed digital filter.

You cannot use a digital filter as an anti-aliasing filter. Anti-aliasing has to be done in hardware before the ADC.