Butterworth lowpass filter design code

Hello everyone, I wrote a simple code to analyze an accelerometric signal in the frequency domain and I saw that the magnitudes over the 300 Hz are quite negligible. I used a Chebyshev type 1 lowpass filter and it works:

%%Design a Lowpass IIR Filter 
N=7;
Fp=300;
Ap=1;
h=fdesign.lowpass('N,Fp,Ap', N, Fp, Ap, Fs);
d=design(h, 'cheby1');

%%Apply the filter to to Smooth out the Signal 
xfilter = filter(d,x2);

%%Overlay the filtered signal on the original signal. 
% Filtered signal is delayed
figure;
plot(t2,x2,'b',t2,xfilter,'r');
grid on;
legend({'Original Signal','Filtered Signal'});
%set(gcf,'NumberTitle','Off', 'Name','Filtered Signal vs. Actual Signal');

%%Compare the original signal and delay compensated filtered signal 
figure;
xfiltfilt = filtfilt(d.sosMatrix,d.ScaleValues,x2);
plot(t2,x2,t2,xfiltfilt);
grid on
legend({'Original Signal','Actual (filtered and delayed signal)'});

Now, I'd like to use a Butterworth lowpass filter: how can I modify my script? Thank you very much!

Answer 1

[Star Strider]

I would just substiture 'butter' here:

d=design(h, 'butter');

I would also add 'Ast' to the fdesign.lowpass parameters for a Butterworth design.

Also, use filtfilt for phase-neutral filtering, not filter, so your*|‘xfilter’|* assignment becomes:

xfilter = filtfilt(d,x2);

This applies to all filter designs, so try it with your Chebyshev Type I filter as well. The results will be different, perhaps noticeably so.

[Guglielmo Giambartolomei]

Thank you Star Strider! I wrote this simple code for a Butterworth filter (I didn't use the design toolbox):

    % Butterworth filter
    Fc = 300;
    Fs = 2400;
    [b,a] = butter(10,Fc/(Fs/2));
    figure;
    freqz(b,a)
    dataIn = x2;

    %%Apply the filter to to Smooth out the Signal 
    xfilter = filter(b,a,dataIn);

    %%Overlay the filtered signal on the original signal. 
    % Filtered signal is delayed
    figure;
    plot(t2,x2,'b',t2,xfilter,'r');
    grid on;
    legend({'Original Signal','Filtered Signal'});

    %%Compare the original signal and delay compensated filtered signal 
    figure;
    xfiltfilt = filtfilt(b,a,x2);
    plot(t2,x2,t2,xfiltfilt);
    grid on
    legend({'Original Signal','Actual (filtered and delayed signal)'});

What do you think about it? Thanks!

[Star Strider]

I would use buttord to calculate the optimal filter order, and convert it to second-order-section form for stability. My filter design procedure for IIR filters is here: How to design a lowpass filter for ocean wave data in Matlab?

[Guglielmo Giambartolomei]

Thank you for sharing Star Strider.

[Star Strider]

My pleasure.

If my Answer helped you. please Accept it.