Hello everyone, I have a matlab problem and I don't know how to go about it.The question goes thus: Using a matlab code prove that for discrete time sinusoids whose frequencies are seperated by an integer multiple of 2*pi are identical. Pleas

Hello everyone,

I have a matlab problem and I don't know how to go about it.The question goes thus:

Using a matlab code prove that for discrete time sinusoids whose frequencies are seperated by an integer multiple of 2*pi are identical.

Please help........................................................

Answer 1

[Youssef Khmou]

hi,

I think you mean that two sinusoidal functions whose phases are separated by integer multiple of 2*pi are identical :

 Fs=40;         % sample rate
 f=15;          % fundamental frequency
 t=0:1/Fs:2-1/Fs;
 b=2*pi*2;         % phase multiple of 2*pi
 y1=sin(2*pi*t*f);
 y2=sin(2*pi*t*f+b);
 figure, plot(t,y1,t,y2,'r')
 rmse=sqrt(mean((y1-y2).^2));
 norm(y1-y2);

now change b to another value, you will realize that they are not identical anymore .

Answer 2

[Muthu Annamalai]

Usually forum members don't provide canned homework solutions. You have a better chance to receive help when you show your work.

Having said, that you can learn solution to your problem by reading the help for FFT function at FFT Example section.

Answer 3

[Image Analyst]

What are identical? Surely sine waves of different frequencies are not identical. A sine wave of 314 hertz is not identical to one at 628 hertz or one at 942 Hertz. What is supposed to be identical here? They could be identical if you subsampled them at the proper subsampling rate.

[Matt J]

The OP mentions "discrete sinusoids". I think the idea is that

 a(n) = sin(2*pi*f*n)

is identical to

 b(n) = sin(2*pi*(f+m)*n)

for any integer m

[Image Analyst]

And for only certain specific f and n, not for any and all values. A simple subtraction would work to show that they're equal at certain n indexes.