Frequency based on acceleration data

Hi,

I want to find the frequency during testing based on the acceleration data collected using accelerometer. I already try several method using MATLAB but I'm not sure if mine is correct. Different method give me different frequency value. For the info, the machine frequency is 6.67 Hz. I attach the code and file for reference.

clc;
clear all;
close all;

Time = xlsread('Book5','A1:A585'); 
Acceleration = xlsread('Book5','B1:B585'); 

n = length(Acceleration); 
Ts = Time(2)-Time(1);           
Fs = 1/Ts;                       
NFFT = 2^nextpow2(n);           
Y = fft(Acceleration,NFFT)/n;
f = Fs/2*linspace(0,1,NFFT/2+1);
Iv = 1:length(f);  

figure(1)
plot(f,abs(Y(Iv))) 
xlabel('Frequency (Hz)')
ylabel('Amplitude (m)')

num=csvread("Book5.csv");                                                                            
Fs = 1/mean(diff(num(:,1)));                                    
Fn = Fs/2;                                                    
Tr = linspace(num(1,1), num(1,end), size(num,1));              
Dr = resample(num(:,4), Tr);                               
Dr_mc  = Dr - mean(Dr,1);                                       
FDr_mc = fft(Dr_mc, [], 1);                                     
Fv = linspace(0, 1, fix(size(FDr_mc,1)/2)+1)*Fn;                
Iv = 1:numel(Fv);                                               
figure(13)
plot(Fv, abs(FDr_mc(Iv,:))*2)
grid
xlabel('Frequency (Hz)')
ylabel('Amplitude')

Thank you.

Answer 1

[Mathieu NOE]

hello

I tried to do my best finding the fft length and overlap that gives me the best info - as your signal is quite unstationnary

this is what I could tell from your data

Spectrogram : look at the red area as this is the dominant frequencies (depend of time)

the amplitude (color) is expressed in dB (log scale of amplitude)

Averaged FFT spectrum , basicaly the time average of the spectrogram , here you lose the information of time dependance but you can probably find your frequencies (no 6.67 Hz found ! )

Code

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

filename = ('Book5.xlsx'); 
data = readmatrix(filename);
time = data(:,1);
signal = data(:,2);
dt = mean(diff(time));
Fs = 1/dt; % sampling rate 

[samples,channels] = size(signal);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 200;    % 
OVERLAP = 0.95;  % must be between 0 and 0.95

% spectrogram dB scale
spectrogram_dB_scale = 80;  % dB range scale (means , the lowest displayed level is XX dB below the max level)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% options 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% if you are dealing with acoustics, you may wish to have A weighted
% spectrums 

% option_w = 0 : linear spectrum (no weighting dB (L) )
% option_w = 1 : A weighted spectrum (dB (A) )
option_w = 0;

%% decimate (if needed)
% NB : decim = 1 will do nothing (output = input)
decim = 1;
if decim>1
    for ck = 1:channels
    newsignal(:,ck) = decimate(signal(:,ck),decim);
    Fs = Fs/decim;
    end
   signal = newsignal;
end
samples = length(signal);
time = (0:samples-1)'*1/Fs;

%%%%%% legend structure %%%%%%%%
for ck = 1:channels
    leg_str{ck} = ['Channel ' num2str(ck) ];
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 1 : time domain plot
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1),plot(time,signal);grid on
title(['Time plot  / Fs = ' num2str(Fs) ' Hz ']);
xlabel('Time (s)');ylabel('Amplitude');
legend(leg_str);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2 : averaged FFT spectrum
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[freq, sensor_spectrum] = myfft_peak(signal,Fs,NFFT,OVERLAP);

% convert to dB scale (ref = 1)
sensor_spectrum_dB = 20*log10(sensor_spectrum);

% apply A weigthing if needed
if option_w == 1
    pondA_dB = pondA_function(freq);
    sensor_spectrum_dB = sensor_spectrum_dB+pondA_dB;
    my_ylabel = ('Amplitude (dB (A))');
else
    my_ylabel = ('Amplitude (dB (L))');
end


figure(2),plot(freq,sensor_spectrum_dB);grid on
df = freq(2)-freq(1); % frequency resolution 
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(df,3) ' Hz ']);
xlabel('Frequency (Hz)');ylabel(my_ylabel);
legend(leg_str);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 3 : time / frequency analysis : spectrogram demo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for ck = 1:channels
    [sg,fsg,tsg] = specgram(signal(:,ck),NFFT,Fs,hanning(NFFT),floor(NFFT*OVERLAP));  

    % FFT normalisation and conversion amplitude from linear to dB (peak)
    sg_dBpeak = 20*log10(abs(sg))+20*log10(2/length(fsg));     % NB : X=fft(x.*hanning(N))*4/N; % hanning only

    % apply A weigthing if needed
    if option_w == 1
        pondA_dB = pondA_function(fsg);
        sg_dBpeak = sg_dBpeak+(pondA_dB*ones(1,size(sg_dBpeak,2)));
        my_title = ('Spectrogram (dB (A))');
    else
        my_title = ('Spectrogram (dB (L))');
    end

    % saturation of the dB range : 
    % saturation_dB = 60;  % dB range scale (means , the lowest displayed level is XX dB below the max level)
    min_disp_dB = round(max(max(sg_dBpeak))) - spectrogram_dB_scale;
    sg_dBpeak(sg_dBpeak<min_disp_dB) = min_disp_dB;

    % plots spectrogram
    figure(2+ck);
    imagesc(tsg,fsg,sg_dBpeak);colormap('jet');
    axis('xy');colorbar('vert');grid on
    df = fsg(2)-fsg(1); % freq resolution 
    title([my_title ' / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(df,3) ' Hz / Channel : ' num2str(ck)]);
    xlabel('Time (s)');ylabel('Frequency (Hz)');

end

function pondA_dB = pondA_function(f)
	% dB (A) weighting curve
	n = ((12200^2*f.^4)./((f.^2+20.6^2).*(f.^2+12200^2).*sqrt(f.^2+107.7^2).*sqrt(f.^2+737.9^2)));
	r = ((12200^2*1000.^4)./((1000.^2+20.6^2).*(1000.^2+12200^2).*sqrt(1000.^2+107.7^2).*sqrt(1000.^2+737.9^2))) * ones(size(f));
	pondA = n./r;
	pondA_dB = 20*log10(pondA(:));
end


function  [freq_vector,fft_spectrum] = myfft_peak(signal, Fs, nfft, Overlap)
% FFT peak spectrum of signal  (example sinus amplitude 1   = 0 dB after fft).
% Linear averaging
%   signal - input signal, 
%   Fs - Sampling frequency (Hz).
%   nfft - FFT window size
%   Overlap - buffer percentage of overlap % (between 0 and 0.95)

[samples,channels] = size(signal);

% fill signal with zeros if its length is lower than nfft
if samples<nfft
    s_tmp = zeros(nfft,channels);
    s_tmp((1:samples),:) = signal;
    signal = s_tmp;
    samples = nfft;
end

% window : hanning
window = hanning(nfft);
window = window(:);

%    compute fft with overlap 
 offset = fix((1-Overlap)*nfft);
 spectnum = 1+ fix((samples-nfft)/offset); % Number of windows
%     % for info is equivalent to : 
%     noverlap = Overlap*nfft;
%     spectnum = fix((samples-noverlap)/(nfft-noverlap));	% Number of windows

    % main loop
    fft_spectrum = 0;
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft),:).*(window*ones(1,channels));
        fft_spectrum = fft_spectrum + (abs(fft(sw))*4/nfft);     % X=fft(x.*hanning(N))*4/N; % hanning only 
    end
    fft_spectrum = fft_spectrum/spectnum; % to do linear averaging scaling

% one sidded fft spectrum  % Select first half 
    if rem(nfft,2)    % nfft odd
        select = (1:(nfft+1)/2)';
    else
        select = (1:nfft/2+1)';
    end
fft_spectrum = fft_spectrum(select,:);
freq_vector = (select - 1)*Fs/nfft;
end

[MARLIANA HAFIZA]

thank you for your help. Its seems the output consist of various frequency and quite overlapping that's why the output are unstationnary. May I know what does it mean by the avereage FFT spectrum value ? It is the average frequency from all frequency values that have been collected ?

[Mathieu NOE]

in terms of signal processing, you can decide wheter you make

• one fft computation with the fft length equal to the signal length (and in this case there is of course no averaging
• or you split your signal into smaller chunks (buffers) and you do the fft on each buffer and then you average the spectra ; this reduce the impact of spurious / non correlated noises on your resulting spectrum. You can increase the number of averages by introducing some overlap between buffers. For spectrograms, having / increasing the overlap makes the rendering more progressive (smooth) at the expense of more fft computations
• also the fft spectrum frequency resolution df depends of the fft length nfft and sampling rate (Fs) :
• df = Fs / nfft, so for a given Fs, if you want more averages you will have to reduce nfft (and maybe use a higher overlap), but globally you cannot have a the same time a very small frequency resolution and lot of averages. It's all about finding the best compromise depending of your signal characteristics (stationnary or not)

[Mathieu NOE]

hello again

did my submission fullfil your request ?