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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    0
    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.
     
  2. nsaspook

    AAC Fanatic!

    Aug 27, 2009
    2,907
    2,168
    A complex sinusoidal is simply the same as the I/Q (phase-quadrature) representation of the signal.

    [​IMG]

    A plot of a complex sinusoid versus time, consists of one frequency [​IMG].
     
  3. MrAl

    Well-Known Member

    Jun 17, 2014
    2,429
    490

    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
    12,440
    3,361
    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) ]
     
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