How to Integrate a vector?

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

Answer 1

[Star Strider]

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;

[Fourier]

So you mean tv is my time vector and I can simply integrate over time , let's say t=2 then y= 2/Fs*trapz(Input)

[Star Strider]

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]

okay many thanks, so finally can you tell how to integrate from tv=2 to tv=4

[Star Strider]

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]

Thanks, very helpfully !

[Star Strider]

@Peter Druzba — My pleasure!