how to generate three independent sinusoidal signal in matlab?

Guys,

does anyone know how to generate three independent signal in MatLab. If it's sinusoidal, would be great.

Thanks,

Answer 1

[Youssef Khmou]

sin waves with different frequencies :

 Fs=20;
 f1=2;
 f2=4;
 f3=9;
 t=0:1/Fs:10-1/Fs;
 y1=sin(2*pi*f1*t);
 y2=sin(2*pi*f2*t);
 y3=sin(2*pi*f3*t);

[Ethen]

are they independent? how can I check that? thanks

[Image Analyst]

What is your definition of independent? If you change the y1 variable, obviously y2 and y3 don't change, so in that sense y1 is independent of y2 and y3. Though they are all correlated, the correlation value being dependent on the location where you're looking.

[Youssef Khmou]

Yes they are independent

 Y=[y1',y2',y3'];
 R=cov(Y)

All Rij are null.

[Ethen]

uncorrelatedness doesn't lead to independence unless the distribution is gaussian.

[Rick Rosson]

One possibility is to ensure that all three signals are mutually orthogonal. For pure tone sine waves, a sufficient condition for orthogonality is to set the three frequencies such that all are integer multiples of a common fundamental:

   f0 = 5;
   f1 = 1*f0;
   f2 = 2*f0;
   f3 = 3*f0;

or better:

   f0 = 5;
   f = f0*(1:3);

[Youssef Khmou]

Correct. You can calculate theirs scalar product, example :

   dot(y1,y2)
   dot(y2,y2)