Going from the time doain to the frequncy domain, why the amplitude of the signal is increased?

Hi All,

I have a time-depended signal (vector signal.mat and time.mat). In particular, I know the signal values are accelerations, sampled at 200 Hz and the signal is a real machine output so it contains noise.

My aim is to go from the time domain to the frequency domain, to see the spectrum and "later" to filter the data from the noise.

So, I wish to plot my signal amplitude and phase in the frequency domain and for this I have use the FFT function.

However, I think I did something wrong as I am expecting the signal amplitude in the frequency domain should be in the same range as is the time domain. (For example, if my object accelerates at a max of 5.5 m/s^2 in the time domain, then the same max value should be seen in the frequency domain) But, as you can see from the plots attached, the max acceleration in the time domain is about 5.5 m/s^2. But in the frequency domain the max amplitude is about 200 m/s^2.

That CANNOT BE RIGHT? right????

Below I attached my code so far. Please help me if you can

PS: I am not a great matlab user so please try to think that I am new to this software

Thanks in advance

%%BEGINNING OF THE PROGRAM

load('time.mat');   % load the time domain variable 

load('signal.mat'); % load the time-dependent variable (an acceleration in this case)

figure(1)           % The following commands plt the signal in the time domain

plot(time,signal);

title('Plot of the signal in the Time Domain')

xlabel('time    (sec) ')

ylabel('m/s^2')

grid on

%%Signal Processing 

DFT_signal = fft(signal);   % Calculate the Discreat Fourier Transform (DFT) of the signal using the Fast Fourier Transform algorithm

N = length(time);       % Number of Samples of the signal in the time domain

ts = time(2)-time(1);   % Calculate the Sampling Time (sec)

fs = 1/ts;              % Calculate the Sampling frequency (Hz) of the signal in the time domain

fuF = fs/N;             % Calculate the Fundamental Frequency (Hz) of the signal in the frequency domain

f = [0:fuF:(fs-fuF)/2]';    % Create the frequency domain (Hz). Note that the domain is N/2 because of the DFT symmetry domain.

MAG_DFT = abs(DFT_signal(1:N/2));     % Magnitude of the Signal DFT (m/s^2 ??????)

PHASE_DFT = imag(DFT_signal(1:N/2));   % Phase of the Signal DFT

subplot(2,1,1)           % The following commands plt the DFT of the signal in the frequency domain

plot(f,MAG_DFT);         % using a figure with two plots    

title('Plot of the Signal DFT Magnitude in the Frequency Domain')

xlabel('Frequency    (Hz) ')

ylabel('m/s^2')

grid on

subplot(2,1,2)      

plot(f,PHASE_DFT/pi()*180);

title('Plot of the Signal DFT Phase in the Frequency Domain')

xlabel('Phase   (rad)')

ylabel('m/s^2')

grid on

Answer 1

[Wayne King]

You're missing the scaling of the fft() output by the length of the input signal. That is likely the biggest contributor to why your scale is off. See how a unit amplitude sine wave below ends up as unit magnitude in the frequency domain.

   Fs = 1000;
   t = 0:1/Fs:1-1/Fs;
   x = cos(2*pi*100*t);
   L = length(x);
   xdft = fft(x)/L;
   xdft = xdft(1:L/2+1);
   xdft(2:end-1) = 2*xdft(2:end-1);   
   plot(abs(xdft))

[Giuseppe Naselli]

Hi Wayne and thanks for you answer.

I modified my line DFT_signal = fft(signal) with your suggestion

DFT_signal = fft(signal)/N

but now the signals are too small (see picture attached)

So I still need help with this

[Wayne King]

Are you able to attach your time data?

[Giuseppe Naselli]

Hi Waine,

sorry for the late reply but I did not get an email when you answered.

I hope it is not too late.

I have copied the signal and the time variable together with my code on dropbox (I do not know how I can attach files other than pictures here)

https://www.dropbox.com/sh/r9yntj2d6vpq0bs/7r0T_TjFNU

However, the time variable is just from 0 to 59.995 sec in step of 0.005sec.

Thanks for your help so far

G

DropBox

[Ella]

please share the final solution with us Im having the same problem and cant solve it