How to design a 3rd order butterworth bandpass filter characteristic which will then be used for the dfilt.df1tsos function?

I have to create a 3rd order butterworth bandpass characteristic [10 12] (Hz). Thereafter, I need to use the biquad second-order section filter function (dfilt.df1tsos) and filter the data with the filter function.

I do have the following code for a 2-order filter:

Fs = 5000; Fn = Fs/2; Lf = 10 Hf = 12

[z,p,k] = butter(1,[Lf Hf]/(Fn), 'bandpass');

[s,g] = zp2sos(z,p,k);

Hd = dfilt.df1tsos(s,g)

fvtool (Hd)

y = filter(Hd, data');

I am not sure how to handle the combination of bandpass butterworth characteristic and the biquad filter since I have little experience with filtering.

Would be great if anyone provides help.

Answer 1

[Binaya]

Hi Patrick

Your approach is correct. To design a 3rd order Butterworth bandpass filter, you just need to modify the "butter" function of the MATLAB in your code to the following:

% Design a 3rd order Butterworth bandpass filter
[z, p, k] = butter(3, [Lf Hf] / Fn, 'bandpass');

Also note that the 3rd order Butterworth filter will also include the first-order and second-order characteristics in its SOS(second-order section).

You can refer to the following documentation links for more details:

1. "butter": https://www.mathworks.com/help/signal/ref/butter.html
2. "zp2sos" : https://www.mathworks.com/help/signal/ref/zp2sos.html
3. "design", you can refer to 'design' to apply a design method to a filter specification object: https://www.mathworks.com/help/dsp/ref/design.html

Hope this helps.