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

Thread Starter

spark360z

Joined Jul 27, 2012
10
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!
 

Wendy

Joined Mar 24, 2008
23,415
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).
 

MrChips

Joined Oct 2, 2009
30,712
My question is, what does F(jω) represent in frequency domain?

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?
You are correct.

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