MATLAB: Convert the time domain signal into frequency domain signal

freqency domaintime domain

Hi, I have represented the acceleration data of 3 axes(x, y, and z) in time domain as shown in the Graph

I would like to extract from the acceleration data some measurements (e.g. mean, energy, entropy and correlation) in the frequency domain. Therefore, I applied FFT transform in order to convert the time domain signal into frequency domain signal.

    xx=  fft(x_Segments{1});
    plot(xx)
    yy=  fft(y_Segments{1});
    plot(yy)
     zz=  fft(z_Segments{1});
     plot(zz)

However, the resulted graphs make no sense( so strange) which is not expected at all !! This is an example of the frequency domain signal of the x-axis.

Note, x_Segments, y_Segments, and z_Segments contain the data of X, Y, Z axes respectively

As we can see the graph doesn't make sense, so, is there any steps that I should follow before using the FFT function to get the expected frequency domain signal?

I really appreciate your help guys. thanks

Best Answer

See this version of the documentation for fft.

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MATLAB: How to create low pass filter for audio file

You gave enough information for the Signal Processing Toolbox (with a bit of help from me) to be able to design your filter:

Fs  = 8000;                                 % Sampling Frequency (Hz)
Fn  = Fs/2;                                 % Nyquist Frequency
Fco =   20;                                 % Passband (Cutoff) Frequency
Fsb =   30;                                 % Stopband Frequency
Rp  =    1;                                 % Passband Ripple (dB)
Rs  =   10;                                 % Stopband Ripple (dB)
[n,Wn]  = buttord(Fco/Fn, Fsb/Fn, Rp, Rs);  % Filter Order & Wco
[b,a]   = butter(n,Wn);                     % Lowpass Is Default Design
[sos,g] = tf2sos(b,a);                      % Second-Order-Section For STability
figure(1)
freqz(sos, 2048, Fs)                         % Check Filter Performance

Then use the filtfilt function to filter your signal.

I chose a Butterworth design, but if you want a steeper cutoff, consider using a Chebychev design instead. You may want to experiment with the design to get the exact result you want with respect to your signal. See the relevant documentation for details.

MATLAB: About Butterworth filter design

You have not clearly stated what you want to do.

You also have problems in your calculations, and your data are not uniformly sampled.

First, you need to use the Signal Processing Toolbox resample (link) function to regularly sample your data. Create a time vector for the resampling (interpolation) as:

tv = linspace(min(date), max(date), size(data,1));

From the documentation:

y = resample(x,tx) resamples the values, x, of a signal sampled at the instants specified in vector tx. The function interpolates x linearly onto a vector of uniformly spaced instants with the same endpoints and number of samples as tx. NaNs are treated as missing data and are ignored.

Second, you are not calculating the sampling interval and therefore the sampling frequency correctly. Calculate them as:

Ts = mean(diff(tv));                                    % Sampling Interval (Days)
Fs = 1/Ts;                                              % Sampling Frequency (1/Day)
Fn = Fs/2;                                              % Nyquist Frequency (1/Day)

Then do a fft (link) on your resampled data to determine the frequencies you want to pass or reject, and specify your filter accordingly. I cannot do that because I do not know what you want to do.

Use the filtfilt function, not filter, to do the actual filtering.

Best Answer

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MATLAB: How to create low pass filter for audio file

MATLAB: About Butterworth filter design

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