# What happens if we multiply a sinusoidal signal with a complex sinusoidal signal

Discussion in 'General Electronics Chat' started by NaveenKori, Sep 23, 2016.

1. ### NaveenKori Thread Starter New Member

Sep 13, 2016
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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?

2. ### nsaspook AAC Fanatic!

Aug 27, 2009
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3,638
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 .

3. ### MrAl Distinguished Member

Jun 17, 2014
3,622
763

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).

4. ### NaveenKori Thread Starter New Member

Sep 13, 2016
8
0

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

5. ### MrChips Moderator

Oct 2, 2009
14,291
4,197
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) ]