Confusion with FFT for a specific part of the whole signal

As a newbie i am working on a signal from an accelerometer and i am trying to produce an fft for a specific part of the whole signal. I am a little bit confused about which code for the fft is the appropriate to use for my case.

here is my code:

clear all

close all

load signal

tvec=noact(:,1);

acc=noact(:,2);

%% ALL SIGNAL

L=length(signal); % Length of signal

t_max=max(signal(:,1)); % Tmax

Fs=L/t_max; % Sampling Rate

T = 1/Fs; % Sample time

%% PART OF SIGNAL

trace1=signal(Fs*25:Fs*32,:); % select part of signal

matrice1=trace1(:,2); % accelerations column

L1=length(matrice1); % Length of trace (number of samples)

t1 = (0:L1-1)*T; % Time vector

% Frequency vector

f1=(0:Fs/length(matrice1):(length(matrice1)-1)*Fs/length(matrice1));

FrecSign=abs(fft(matrice1))*T;

figure

plot(FrecSign);

xlabel Frequency(Hz)

ylabel Amplitude

title 'FFT'

or

NFFT = 2^nextpow2(L); % Next power of 2 from length of matrice1

Y = fft(matrice1,NFFT)/L;

f = Fs/2*linspace(0,1,NFFT/2+1); % create frequency vector

figure % Plot single-sided amplitude spectrum.

plot(f,2*abs(Y(1:NFFT/2+1)))

title('Single-Sided Amplitude Spectrum of y(t)')

xlabel('Frequency (Hz)')

ylabel('|Y(f)|')

Thanks in advance

Answer 1

[Star Strider]

I cannot follow our code.

However, you cannot ‘produce an fft for a specific part of the whole signal’, since you have to take the fft (link) of the entire signal if you want valid data.

If you want to view only part of the signal, use the axis function to limit the frequency (here x) axis to the range you want.

If you want to eliminate specific frequencies from your accelerometer signals (for example a constant offset, low-frequency baseline variations, high-frequency noise), use a discrete filter. There are several ways to to this, with the designfilt function being the easiest to use (in my opinion).

[Ancalagon8]

Star Strider thanks for your answer.. I want to choose a part of the initial signal, from 25 sec to 32 second ( code: trace1=signal(Fs*25:Fs*32,:); ) Assuming i produce the fft for the whole signal, how is it possible to detect which part of the fft corresponds to trace1(25 sec to 32 second).

As for the code, is NFFT calculation necessary for FFT's production or i can by-pass it?

[Star Strider]

My pleasure.

You can select the part of your signal from 25 to 32 seconds and then do a fft (link) on it. You then consider that section to be your entire signal. You can get the frequency resolution of your original complete data by zero-padding your 7-second segment to the length of your original signal. You can do this by specifying the length of the original vector as the second argument (the ‘NFFT’ argument) to the fft function. I would use the ‘NFFT’ argument in that situation, because higher frequency resolution is usually better.

I may have misunderstood earlier in that I thought you wanted to do the fft on all of your signal data, and then somehow choose the section derived from the 25 to 32 seconds segment from it. The only ways you can do a time-frequency analysis are with the Signal Processing Toolbox spectrogram function or with wavelets. (I am not yet sufficiently familiar with the Wavelet Toolbox to deal with it on MATLAB Answers.)

[Star Strider]

Sirius8’s Answer moved here:

Yes, first i choose the signal part and then produce the fft. My fault, maybe i did not make it clear from the beggining. So:

trace1=signal(Fs*25:Fs*32,:); % select part of signal

matrice1=trace1(:,2);

NFFT = 2^nextpow2(L);

Y = fft(matrice1,NFFT)/L;

f = Fs/2*linspace(0,1,NFFT/2+1);

figure

plot(f,2*abs(Y(1:NFFT/2+1)))

The above code is right?

[Star Strider]

I am not certain about your indexing here:

trace1=signal(Fs*25:Fs*32,:); % select part of signal

You may want to consider using the round (or similar) function, for example round(Fs*25):round(Fs*32) to be certain the subscripts are integers.

However the rest of the code (calculating and plotting the fft) appears to be correct.

[Ancalagon8]

Fine thank you! I want also to plot a psd but in x axis to have frequencies and not normalized frequencies. I used

[PSDx,fx] = periodogram(x,[],[],Fs,'power');

plot(fx,PSDx)

Is it correct?

Thanks again!

[Star Strider]

My pleasure.

It appears correct to me. You have to determine if it produces the results you want.

[Brad]

Hi Star

I have a question regarding your answer here, I would very much appreciate it if you answer my question.

https://uk.mathworks.com/matlabcentral/answers/728853-why-is-fft-of-one-part-and-the-entire-signal-the-same

Thank you

Brad

[Star Strider]

Done!

And thank you for accepting it!

Answer 2

[Ancalagon8]

One last question. In [PSDx,fx] = periodogram(x,[],[],Fs,'power');

x should be

i) the original signal (acc over time)?

ii) the original signal (only the acc column)

iii) the fft?

Thanks in advance!

[Star Strider]

I’m not sufficiently certain that I understand your data well enough to address that. I would analyse one variable at a time in each call to periodogram, so most likely (ii).

Answer 3

[Ancalagon8]

So in order to produce a periodogram, my input x should be the acceleration vector.

[Star Strider]

Yes, if you want the periodogram of your acceleration data.