Time + Acceleration Fourier transform into Amplitude + Frequency

I am trying to transform measured data from time and accelerations into amplitude and frequency, but I really dont understand the process. I have this:

g=9.81

A = importdata('220927_1.txt')

A = A.data

% Front Left sprung mass

B = [A(:,1),A(:,3).*g]

N = pow2(nextpow2(length(B)));

y = fft(B,N);

plot(1:N,abs(y))

Time = B(:,1); % Time (s)

Acceleration = B(:,2); % Acceleration (m/s^2)

n = length(Acceleration);

Ts = Time(n)-Time(1); % Sample Time

Fs = 1/Ts; % Sampling Frequency

NFFT = 2^nextpow2(n); % Next power of 2 from length of data

Y = fft(Acceleration,NFFT)/n;

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

plot(f,abs(Y))

xlabel('Frequency (Hz)')

ylabel('Amplitude (m)')

I copied the script for Fourier transform from another support but I dont know how to fix it for my application.

Additionally I was recommended to reduce the noise which I didnt search yet, but its not neccessary to answer that here.

I attached the measurement file. For sprung mass (vehicle body) there should be natural frequency somewhere around 1 to 2 Hz, so there should be peak value in ploted result. (for unsprung its around 10 Hz)

Answer 1

[Star Strider]

The ‘Time’ values are not unique (they likely need an additional digit of precision) so they had to be processed by taking the mean of the unique values for both variables. The rest of the code needed a bit of tweaking to get it to work correctly. The signal has broadband noise, so a frequency-selective filter will not remove much of it. I experimented by filtering it with the sgolayfilt function since you mentioned filtering, however filtering may not be necessary if yoiu are only interested in the spectral qualities of the signal.

Try something like this —

Uz = unzip('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1141115/220927_1.zip');
T1 = readtable(Uz{1}, 'VariableNamingRule','preserve')

T1 = 104550×15 table
    Time     Vehicle Speed    FL Sprung acceleration    FR Sprung acceleration    RL Sprung acceleration    RR Sprung acceleration    FL Unsprung acceleration    FR Unsprung acceleration    RL Unsprung acceleration    RR Unsprung acceleration    Bellow pressure RL    Bellow pressure RR    Acceleration X    Acceleration Y    Acceleration Z
    _____    _____________    ______________________    ______________________    ______________________    ______________________    ________________________    ________________________    ________________________    ________________________    __________________    __________________    ______________    ______________    ______________

        0          0                  -0.089                    -0.034                    -0.034                    0.126                      1.156                       0.755                       0.736                       1.528                    2.341                 2.275               -0.594            -0.183            -1.857    
        0          0                  -0.089                    -0.035                    -0.036                    0.129                      1.137                       0.753                       0.749                       1.543                    2.338                 2.275               -0.595            -0.185            -1.857    
        0          0                  -0.089                    -0.037                    -0.037                     0.13                      1.148                        0.76                       0.762                       1.555                    2.337                 2.271               -0.596            -0.185            -1.857    
    0.001          0                  -0.091                    -0.039                    -0.038                    0.132                      1.139                       0.747                       0.792                       1.569                    2.344                 2.264               -0.597            -0.186            -1.858    
    0.001          0                  -0.091                     -0.04                    -0.037                    0.133                      1.145                       0.754                        0.78                       1.567                    2.334                  2.27               -0.596            -0.182            -1.856    
    0.001          0                  -0.092                    -0.043                    -0.032                    0.135                      1.138                       0.743                       0.781                       1.534                    2.344                 2.271               -0.595            -0.183            -1.858    
    0.001          0                  -0.092                    -0.043                    -0.029                    0.133                      1.147                       0.752                       0.783                       1.542                    2.345                 2.269               -0.595            -0.181            -1.857    
    0.001          0                  -0.094                    -0.046                    -0.024                    0.132                      1.136                       0.762                       0.784                       1.531                    2.335                 2.272               -0.594            -0.184             -1.86    
    0.002          0                  -0.095                    -0.047                    -0.021                     0.13                      1.126                       0.775                       0.771                       1.526                    2.334                 2.267               -0.595            -0.181            -1.857    
    0.002          0                  -0.095                    -0.047                    -0.017                    0.131                      1.119                       0.807                        0.76                       1.552                    2.329                 2.269               -0.595            -0.181            -1.856    
    0.002          0                  -0.096                    -0.048                    -0.011                    0.129                      1.118                       0.799                       0.761                       1.559                    2.348                 2.275               -0.593            -0.179            -1.853    
    0.002          0                  -0.094                     -0.05                    -0.008                    0.128                      1.127                       0.803                        0.78                        1.54                    2.337                 2.266               -0.597            -0.178            -1.856    
    0.002          0                  -0.095                     -0.05                    -0.007                    0.128                      1.092                       0.786                        0.75                       1.566                    2.336                 2.272               -0.597            -0.176            -1.856    
    0.003          0                  -0.094                    -0.049                    -0.006                    0.126                      1.098                       0.772                       0.739                       1.549                    2.336                 2.276               -0.597            -0.175            -1.856    
    0.003          0                  -0.095                    -0.049                    -0.003                    0.128                      1.111                       0.777                       0.713                       1.555                    2.332                 2.274               -0.597            -0.174            -1.855    
    0.003          0                  -0.095                    -0.049                    -0.004                    0.126                      1.082                       0.792                       0.678                       1.562                    2.337                 2.272               -0.597            -0.172            -1.856    

g=9.81;
t = T1{:,1};
FLSA = T1{:,3}*g;

[Ut,~,ix] = unique(t, 'stable');
C = accumarray(ix, (1:numel(t)), [], @(x){mean([t(x),FLSA(x)])});       % Aggregate Repeated 'Time' Values
M = cell2mat(C);
ta    = M(:,1);
FLSAa = M(:,2);

Ts = mean(diff(ta));
Fs = 1/Ts

Fs = 1.0000e+03

% Tssd = std(diff(ta))

figure
plot(t,FLSA)
grid
xlabel('t')
ylabel('FLSA')
title('Original')

figure
plot(ta,FLSAa)
grid
xlabel('t')
ylabel('FLSA')
title('Aggregated')

FLSAa_filt = sgolayfilt(FLSAa, 3, 51);                  % Optional

figure
plot(ta,FLSAa_filt)
grid
xlabel('t')
ylabel('FLSA')
title('Aggregated & Filtered')

Time = ta; % Time (s)
Acceleration = FLSAa_filt; % Acceleration (m/s^2)
n = numel(Acceleration); 
Ts = Time(n)-Time(1);            % Sample Time
Fs = 1/Ts;                       % Sampling Frequency
NFFT = 2^nextpow2(n);            % Next power of 2 from length of data
Y = fft(Acceleration-mean(Acceleration),NFFT)/n;
f = Fs/2*linspace(0,1,NFFT/2+1);
Iv = 1:numel(f);

figure
plot(f,abs(Y(Iv))*2) 
grid
xlim([0 0.005])
xlabel('Frequency (Hz)')
ylabel('Amplitude (m)')

Experiment to get the desired result.

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