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

fft simple array

Hi, I have 500k lines of data. One column is time the other sound pressure. I want to run an FFT to get into frequency domain but I'm finding this hard. Then I want convert this to dB and then I'll A-weight this output. Most important is the FFT first. Around 6 seconds of data sampled at 50K Hz. rapidly loosing the will to live. Cheers R

Best Answer

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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