design LPF using Filter with Butterworth

how should i use an analog filter with a Butterworth response of order 3, to design a digital IIR low pass filter with 3dB cutoff angular frequency 0.2pi

the aim is to plot the magnitude and the phase response and i knew that i should use butter , freqz , angle functions

Answer 1

[Binaya]

Hi Mohamed

You can follow the below steps to create a lowpass Butterworth filter:

1. Setup the parameters for Butterworth filter i.e. order, cut-off frequency and filter type.
2. Create a Butterworth filter using "butter" function: https://www.mathworks.com/help/signal/ref/butter.html
3. Use "freqz" function to find the frequency response of the filter: https://www.mathworks.com/help/signal/ref/freqz.html

I have also provided an exampe code for you to refer:

N = 3;              % 3rd-order Butterworth filter
Wn = 0.2;           % Normalized cutoff frequency (0.2 corresponds to 0.2*pi radians/sample)
filterType = 'low'; % Lowpass filter

[b, a] = butter(N, Wn, filterType);


numPoints = 1024;           % Number of frequency points
[H, w] = freqz(b, a, numPoints, 'whole'); % Compute frequency response

You can refer to the following MATLAB Answers post for more details on how to plot the frequency response: https://www.mathworks.com/matlabcentral/answers/588133-magnitude-and-phase-response-of-a-lowpass-filter?s_tid=srchtitle

Hope this helps