MATLAB: Vibration Analysis FFT – Cut off frequency

cut-off frequencyfft

Hello everyone,

I am new to Matlab and am currently working on the vibration analysis.

I have measured the acceleration at three different points (Fs = 1000 Hz). Since I have a noise signal in my FFT every 50 Hz (50, 100, 150, … Hz) (PICTURE below) I would like to filter this out. I have tried it with a 6th order low pass Butterworth filter (cut-off frequency 40 Hz), but I am very unsure if this does not change my raw data too much, as there are other eigenmodes at about 60 Hz, 130 Hz and 240 Hz.

Thank you!

Best Answer

A FIR ‘comb’ filter is perfect for this sort of problem! The problem with IIR filters (such as the Butterworth design) is that it is necessary to put them in series to get the desired result.

See if this does what you want:

Fs = 1000;
fcomb = [[47 49.5 50.5 52], [47 49.5 50.5 52]+50, [47 49.5 50.5 52]+100, [47 49.5 50.5 52]+150];
mags = [[1 0 1], [0 1], [0 1], [0 1]];
dev = [[0.5 0.1 0.5], [0.1 0.5], [0.1 0.5], [0.1 0.5]];
[n,Wn,beta,ftype] = kaiserord(fcomb,mags,dev,Fs);
hh = fir1(n,Wn,ftype,kaiser(n+1,beta),'noscale');
figure
freqz(hh, 1, 2^20, Fs)

producing this Bode plot:

I wrote the code so that adding more stopbands should be straightforward. To add more of them, simply add more ‘sections’ to ‘fcomb’, ‘mags’ and ‘dev’. I made the stopbands sufficiently narrow so as not to delete excessive data from your signal that you will likely want to keep. (This is a ‘long’ filter — the order is 560 — however if it is only necessary to run it once for each record, it should still be fairly efficient.) Experiment with it to get different results.

Use the filtfilt function to do the actual filtering.

Related Solutions

MATLAB: How to Butterworth Filter with Bandpass [10 500] with sampling rate 1000

You have to divide your passband and stopband frequencies by the Nyquist frequency to normalise them:

Fs = 1000;                                          % Sampling Frequency
Fn = Fs/2;                                          % Nyquist Frequency
Wp = [10  495]/Fn;                                  % Norrmalised Passband Frequencies
Ws = [5   499]/Fn;                                  % Normalised Stopband Frequencies
Rp =  1;                                            % Passband Ripple (dB)
Rs = 25;                                            % Stopband Ripple (dB)
[n,Wn] = buttord(Wp, Ws, Rp, Rs);                   % Optimal Filter Order
[b,a] = butter(n, Wn);                              % Calculate Filter Coefficients
[sos,g] = tf2sos(b,a);                              % Convert To Second-Order Sections For Stability
figure(1)
freqz(sos, 4096, Fs)                                % Filter Bode Plot

You cannot have any frequency exactly at zero or exactly at the Nyquist frequency, so I designed your passband to be close enough to them to be stable. In your filter, you can also use a high-pass design with a lower cutoff of 10 Hz, since your upper passband is at the Nyquist frequency. The passband and stopband ripple values are necessary to specify in the design but irrelevant to a Butterworth filter. These are acceptable values for most filter designs (for example Chebyshev) that require them.

You would use the ‘sos’ and ‘g’ variables in your actual filter:

filtered_signal = filtfilt(sos, g, signal);

(This design works well in R2016a and should also work in earlier releases.)

MATLAB: How to apply three notch filters of 3rd order

Using IIR filters to do that requires connecting all three in series, and a low-order Butterworth design is likely not going to meet your expectations, since the frequencies are ao close together.

I would use a single FIR filter instead:

Fs = 250;
fcomb = [[49 49.5 50.5 51], [49 49.5 50.5 51]+10, [49 49.5 50.5 51]+12.5];
mags = [[1 0 1], [0 1], [0 1]];
dev = [[0.5 0.1 0.5], [0.1 0.5], [0.1 0.5]];
[n,Wn,beta,ftype] = kaiserord(fcomb,mags,dev,Fs);
hh = fir1(n,Wn,ftype,kaiser(n+1,beta),'noscale');
figure
freqz(hh, 1, 2^20, Fs)
set(subplot(2,1,1), 'XLim',[45 65])                                             % Optional

set(subplot(2,1,2), 'XLim',[45 65])                                             % Optional

Experiment with this to get different results. This designs a 420-order FIR filter, and decreasing the stopband frequency widths will increase its length. (Increasing them would cause them to overlap, and that will throw an error.) It will still be an efficient filtter, however, compared with dascading three IIR filters in a loop.

Use filtfilt to do the actual filtering, Use the same calling convention for the first two arguments as I use in the freqz call.

Best Answer

Related Solutions

MATLAB: How to Butterworth Filter with Bandpass [10 500] with sampling rate 1000

MATLAB: How to apply three notch filters of 3rd order

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