Hi All,

I just wanted to know what happens to the resultant signal that arises from multiplying a pure sinusoidal signal with a complex sinusoidal signal.
Since there is a real and imaginary part in the complex sinusoid, does the pure sinusoid gets multiplied to both the real and complex parts?.
And what happens to the magnitude and frequency if they both have a different frequency?

Thanks in advance.

 

A complex sinusoidal is simply the same as the I/Q (phase-quadrature) representation of the signal.

A plot of a complex sinusoid versus time, consists of one frequency

.

 

Hi All,

I just wanted to know what happens to the resultant signal that arises from multiplying a pure sinusoidal signal with a complex sinusoidal signal.
Since there is a real and imaginary part in the complex sinusoid, does the pure sinusoid gets multiplied to both the real and complex parts?.
And what happens to the magnitude and frequency if they both have a different frequency?

Thanks in advance.

Hello,

What happens is the lower frequency modulates the other frequency, so the result is made up out of the sum and difference frequencies. This happens with any sine waves really that are multiplied together. That's basic AM (amplitude modulation).

 

Hello,

What happens is the lower frequency modulates the other frequency, so the result is made up out of the sum and difference frequencies. This happens with any sine waves really that are multiplied together. That's basic AM (amplitude modulation).

If we were to plot the frequency and phase response, how would it look like?

 

Try to expand

cos A . (cos B + i sin B)

given the following two identities:

cos A. cos B = ½ [ cos(A+B) + cos(A-B) ]

cos A . sin B = ½ [ sin(A+B) - sin (A-B) ]