MATLAB: How to convert engine cylinder pressure data (bar) to frequency (Hz) using FFT or STFT

fftstft

I need to convert incylinder pressure data (bars) to frequnecy (Hz) using time-frequency analysis. The pressure is obtained from 0-720 crank angle degrees.

Best Answer

Save the pressure values (calculated or measured) as a vector, with a vector of the matching sampling times. (A higher sampling frequency is better.) Calculate the sampling frequency from the sampling times, the Nyquist frequency from the sampling frequency, then see the documentation for the fft (link) function to calculate and plot the fft.

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MATLAB: Convert time to frequency domain

To normalise it to a maximum value of 1, divide the Fourier transformed data by the maximum of the Fourier transformed data:

D = load('time_domain.txt');
t = D(:,1);
s = D(:,2);
L = numel(t);                                                   % Vector Length
Ts = mean(diff(t));                                             % Sampling Interval
Fs = 1/Ts;                                                      % Sampling Frequency
Fn = Fs/2;                                                      % Nyquist Frequency
FTs = fft(s)/L;                                                 % Fourier Transform
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                             % Frequency Vector
Iv = 1:numel(Fv);                                               % Index Vector
FTs_plot = abs(FTs(Iv))/max(abs(FTs(Iv)));                      % Normalised Fourier Transform
figure
plot(Fv, FTs_plot)
grid
xlim([0 0.5])

MATLAB: FFT conversion of sound pressure in the time domain.

I prefer this documentation for fft. Specifically note the code between the tip two plot figures.

For your data, I would start with something like this:

(Import data using ‘audioread’, ‘load’, or whatever is appropriate for your file)
t = ...;                                                        % Time Vector
s - ...;                                                        % Signal Vector
L = length(s);                                                  % Signal Length (Obviously)
Ts = mean(diff(t));                                             % Sampling Interval
Fs = 1/Ts;                                                      % Sampling Frequency
Fn = Fs/2;                                                      % Nyquist Frequency
fts = fft(s)/L;                                                 % Fourier Transform
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                             % Frequency Vector
Iv = 1:length(Fv);                                              % Index Vector
figure(1)
subplot(2,1,1)
plot(Fv, abs(fts(Iv))*2)
grid
title('Fourier Transform of ‘s’')
ylabel('Amplitude')
subplot(2,1,2)
plot(Fv, angle(fts(Iv)))
grid
ylabel(Phase (rad)')
xlabel('Frequency (Hz)')

The Nyquist Frequency is the highest resolvable frequency in a sampled signal, so everything scales to it.

NOTE — This is obviously UNTESTED CODE but it should work, with appropriate modifications for your signal and the way your data are organised.

EDIT — Forgot about the decibel conversion. An anonymous function you could use for this (since your data are amplitude and not power) is:

dB = @(amplitude) 20*log10(abs(amplitude));

so you would call it as:

s_dB = dB(fts);

to get the Fourier transform of your data expressed as decibels. Note that decibels are by definition power, not amplitude.

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Related Solutions

MATLAB: Convert time to frequency domain

MATLAB: FFT conversion of sound pressure in the time domain.

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