# Define main frequencies of accelerometer signals

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Sergio RUGGIERI on 21 Dec 2021
Commented: Mathieu NOE on 22 Dec 2021
Dear all,
I have some acceleration data, given by ambient vibrations, as the ones in the attached .txt file (X and Y on the same accelerometer), with a frequency sampling of 200. The main problem is due to a noise that does not allow to recognize the main frequencies of the signal and that pushes to perform some filtering actions (e.g., pass band, low or high pass). Anyway, I'm trying to understand what are the main frequencies of the signals and how to select the values to filter, also considering that PSD does not return clear peaks (an attempt was made with a low pass filter usin 20 Hz as frequency, for which I attached 2 figures, X and Y).
Could anyone help me?
##### 2 CommentsShowHide 1 older comment
Sergio RUGGIERI on 21 Dec 2021
Ok, see the attached PNG files

Mathieu NOE on 21 Dec 2021
hello Sergio
if you are interested in the low frequency range , my liitle code can help you
the quantization noise is quite high but we still can see some emergence of 3 peaks around 14 , 17 and 20 Hz
try this
clc
clearvars
option_notch = 0; % 0 = without notch filter , 1 = with notch filter
fc_notch = 50; % notch freq
option_LPF = 1; % 0 = without low pass filter , 1 = with low pass filter
fc_lpf = 50; % LPF cut off freq
N_lpf = 2; % filter order
option_HPF = 0; % 0 = without high pass filter , 1 = with high pass filter
fc_hpf = 150; % HPF cut off freq
N_hpf = 2; % filter order
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
signal = importdata('dataAcc.txt');
[samples,channels] = size(signal);
% create time vector
Fs = 200;
dt = 1/Fs;
time = (0:samples-1)*dt;
%% notch filter section %%%%%%
% y(n)=G*[x(n)-2*cos(w0)*x(n-1)+x(n-2)]+[2*p cos(w0)*y(n-1)-p^2 y(n-2)]
% this difference equation can be converted to IIR filter numerator /
% denominator
if option_notch ~= 0
w0 = 2*pi*fc_notch/Fs;
p = 0.995;
% digital notch (IIR)
num1z=[1 -2*cos(w0) 1];
den1z=[1 -2*p*cos(w0) p^2];
% now let's filter the signal
signal = filtfilt(num1z,den1z,signal);
end
%% low pass filter section %%%%%%
if option_LPF ~= 0
w0_lpf = 2*fc_lpf/Fs;
% digital notch (IIR)
[b,a] = butter(N_lpf,w0_lpf);
% now let's filter the signal
signal = filtfilt(b,a,signal);
end
%% high pass filter section %%%%%%
if option_HPF ~= 0
w0_hpf = 2*fc_hpf/Fs;
% digital notch (IIR)
[b,a] = butter(N_hpf,w0_hpf,'high');
% now let's filter the signal
signal = filtfilt(b,a,signal);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 512; %
OVERLAP = 0.75;
% dB scale
dB_scale = 40; % 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);
mm = 5*ceil(max(sensor_spectrum_dB,[],'all')/5); % 5 dB rounded max level
ylim([mm-dB_scale mm]);
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))) - 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
sound(signal,Fs);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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
##### 2 CommentsShowHide 1 older comment
Mathieu NOE on 22 Dec 2021
hello Sergio
my pleasure !

R2021a

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