You can get the angular cutoff frequency using desired cutoff frequency by using the below given formula
% fc = 50 is taken as an example
fc = 50;
wc = 2 * pi * fc;
disp(['Angular Cutoff Frequency (wc): ' num2str(wc) ' rad/s']);
If you are using MATLAB app designer for aking your app, then you can add a textbox for fc and add these functions to the app itself with the callback of a button maybe. In the callback function the value of the textbox can be taken for fc value.
Furthur, to find wc using the 3rd order low pass filter, you can use the following code:
fc = 50;
wc = 2 * pi * fc;
b0 = wc^3 * samplingtime^3;
a0 = b0 + 6 * k * wc * samplingtime^2 + 12 * wc^2 * samplingtime + 8;
a1 = 3 * b0 - 24 * wc^2 * samplingtime^2 - 24;
a2 = 3 * b0 + 24 * wc^2 * samplingtime^2 - 24 * k * wc * samplingtime;
a3 = b0 - 6 * k * wc * samplingtime^2 + 12 * wc^2 * samplingtime - 8;
frequencies = linspace(0, fs/2, 1000); % Frequency range to evaluate
H = abs(b0 * exp(-1i*wc*samplingtime) ./ (a0 - a1*exp(-1i*wc*samplingtime) - a2*exp(-2i*wc*samplingtime) - a3*exp(-3i*wc*samplingtime)));
[~, index] = min(abs(H - 0.707));
wc_after_filter = frequencies(index) * 2 * pi;
% Angular cutoff frequency after passing through the filter
disp(['Angular Cutoff Frequency (wc) after filter: ' num2str(wc_after_filter) ' rad/s']);
Hope this helps.
Thanks.
