(Fourier Transform) What does F(j) represent in frequency domain?

Discussion in 'Math' started by spark360z, Nov 30, 2012.

  1. spark360z

    Thread Starter New Member

    Jul 27, 2012
    10
    0
    I'm trying to understand the concept of Fourier transform and get stuck on something very simple.

    My question is, what does F(jω) represent in frequency domain?

    If I have a voltage source v(t), v(t) represents voltage as a function of time, therefore I know the voltage at any given time.

    But in frequency domain, thing seems to be different.

    Let say the transformed signal is V(jω). Let say at ω=2pi(1000), substitute ω in V(jω), suppose I get V(jω)=V(j2pi(1000))=10

    What does "10" represent?

    Is it an amplitude of a sinusoidal at 1000 Hz? Therefore the signal has sinusoidal 1k Hz frequency amplitude=10 as a component?

    I'm not sure about this because the Fourier transform of cosine is Impulse which has amplitude=infinity.

    Please help!
     
  2. spark360z

    Thread Starter New Member

    Jul 27, 2012
    10
    0
    What is the unit of V(jω)? Is it a voltage?
     
  3. Wendy

    Moderator

    Mar 24, 2008
    20,766
    2,536
    It is more of a phase I think. j is an imaginary number (square root of -1). 2ω is 2 ∏ f (2 X Pi X frequency).
     
  4. MrChips

    Moderator

    Oct 2, 2009
    12,442
    3,361
    You are correct.

    See this: http://www.neurophys.wisc.edu/comp/docs/not012.html
     
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