How to Integrate a vector?
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I have an audio file that gives me a long vector when I read it.I am asked to integrate the response over a specific time. My approach is to calculate time 'x' at which the vector reaches its 'ith'element. and then I will integrate it over the time. Can anyone guide
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Star Strider
2017-8-30
To integrate a vector, use the trapz (link) or cumtrapz (link) function, depending on the result you want.
You probably need to calculate a time vector as well. Since audio files are column-major matrices (each column is a different channel), this will work to calcualte the time vector, with ‘y’ being your sound file, and ‘Fs’ your sampling frequency:
tv = linspace(0, size(y,1), size(y,1))'/Fs;
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Fourier
2017-8-30
Star Strider
2017-8-30
Yes, ‘tv’ is your time vector.
I was thinking more along these lines:
y_int = trapz(tv, y);
to integtrate the entire vector, or perhaps:
y_int_2 = trapz(tv(tv <= 2), y(tv <= 2));
to integrate up to ‘tv=2’, or:
y_int = cumtrapz(tv, y);
y_int_2 = y_int(find(tv <= 2, 1, 'last'));
to integrate up to ‘tv=2’.
Fourier
2017-8-30
Star Strider
2017-8-30
Variations on any of the previous syntaxes will work.
One option:
y_int = cumtrapz(tv, y);
y_int_2_4 = y_int(find(tv <= 4, 1, 'last')) - y_int(find(tv <= 2, 1, 'last'));
This is probably more efficient than doing the entire trapz calculation for every interval of interest. I didn’t time it.
Peter Druzba
2019-10-20
Thanks, very helpfully !
Star Strider
2019-10-21
@Peter Druzba — My pleasure!
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