Doubt in Frequency Modulation code

While searching for something FM, I came across this code. I am not able to understand a particular line of code. I have written a comment against that line of code.

fs = 1000;
fc = 200;
t = (0:1/fs:0.2)';
x = sin(2*pi*30*t)+2*sin(2*pi*60*t);
fDev = 50;
int_x = cumsum(x)/fs;  %%% This line of code
xfm = cos(2*pi*fc*t).*cos(2*pi*fDev*int_x)-sin(2*pi*fc*t).*sin(2*pi*fDev*int_x)   ;


I understand the cumsum function but I am not able to understand why is he dividing the integration by Fs i.e. sampling frequency.

1 Answer

When generating the sine wave, the code uses a sampling frequency to establish discrete points in the time domain. It is not continuous. This means the wave is broken up into bins that are exactly 1/fs in size/width.

So if you want a true integral of the wave, you have to take the average density of all the points in a bin by dividing by the sampling frequency.

Hope that helped.