creating spectra of bicycle vibration measurements

Hi. My task is to analyze acceleration signal of bike vibrations. I have to create FFT and PSD spectra. The question is is the code i used for this task correct? Do the spectra that arise make sense?

rawdata=load('time axes modules.dat')
F_x=rawdata(:,4);
D = F_x;                                       % Column Vector
L = numel(D);                                                   % Signal Length
Fs = 8000;                                                        % Sampling Frequency (Hz)
Fn = Fs/2;                                                      % Nyquist Frequency (Hz)
Ts = 1/Fs;                                                      % Sampling Interval (sec)
t = linspace(0, L, L)*Ts; 
rms(D)
rms(D)^2
figure(1)
plot(t, D);
grid
xlabel('Time (sec)')
ylabel('Amplitude')
title('Time axe module Oś');

FTs = fft(D)/L;                                    % Fourier Transform
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                 % Frequency Vector
Iv = 1:length(Fv);                                  % Index Vector
Phs = angle(FTs);
figure(2)
plot(Fv, abs(FTs(Iv))*2)
grid
xlabel('Frequency Hz)')
ylabel('Amplitude m/s^2')

figure(3)
N = length(D);
xdft = fft(D);
xdft = xdft(1:N/2+1);
plot(freq,10*log10(xdft))
grid on
title('Periodogram Using FFT')
xlabel('Frequency (Hz)')
ylabel('Power/Frequency (dB/Hz)')

Answer 1

[Abhinaya Kennedy]

Hi Bartek,

Your code for analysing the acceleration signal of bike vibrations and for creating FFT and PSD spectra is mostly correct, but there are a few improvements that could be made.

• Frequency Vector for PSD Plot: You should define the frequency vector (freq) used in the PSD plot section. It seems you intended to use “Fv” but used “freq” instead.
• PSD Calculation: To calculate the PSD plot correctly, you need to square the magnitude of the FFT components and normalize them for a proper PSD representation.
• FFT Normalization and Scaling: Your FFT normalization and scaling are mostly correct for a single-sided spectrum but ensure this is intentionally excluding the DC and possibly the Nyquist frequency component.

rawdata = M; % Assuming .mat file, not .dat
D = rawdata{:,4}; % This extracts the fourth column as an array if rawdata is a table; 
L = numel(D); % Signal Length
Fs = 8000; % Sampling Frequency (Hz)
Fn = Fs/2; % Nyquist Frequency (Hz)
Ts = 1/Fs; % Sampling Interval (sec)
t = linspace(0, L-1, L)*Ts; % Corrected time vector to start from 0 to (L-1)*Ts

% Plotting the signal
figure(1)
plot(t, D);
grid
xlabel('Time (sec)')
ylabel('Amplitude')
title('Time Axis Module');

% FFT
FTs = fft(D)/L; % Fourier Transform
Fv = linspace(0, Fn, fix(L/2)+1); % Corrected Frequency Vector to match xdft length
Iv = 1:length(Fv); % Index Vector

% Plotting FFT
figure(2)
plot(Fv, abs(FTs(Iv))*2) % Multiplied by 2 for single-sided spectrum
grid
xlabel('Frequency (Hz)')
ylabel('Amplitude (m/s^2)')

% Calculating PSD
N = length(D);
xdft = fft(D);
xdft = xdft(1:fix(N/2)+1); % Ensure xdft is correctly sliced for odd or even N

%%Modified code snippet%%
psd = (1/(Fs*N)) * abs(xdft).^2; % Correct power spectral density calculation
psd(2:end-1) = 2*psd(2:end-1); % Adjust for single-sided spectrum

% Plotting PSD
figure(3);
plot(Fv, 10*log10(psd))
grid on
title('Power Spectral Density Using FFT')
xlabel('Frequency (Hz)')
ylabel('Power/Frequency (dB/Hz)')

Ensure that your frequency vector and normalization factors are correctly applied for both the FFT and PSD plots for accurate spectral analysis.