What Are the Key Components of Fourier Transforms and Their Notation?

[spaghetti3451]

I would like to ask what the following is supposed to convey.


In Fourier transforms, phase, amplitude and frequency are all important.
Usually deal with using complex notation e.g. A exp (-i*phi) = A cos (phi) - iA sin (phi).

Thoughts?

 

[spaghetti3451]

Also, I am wondering

1. why, for a periodic function with its period tending to infinity (a non-cyclic function), the sum in the Fourier series converges to an integral.

2. if the symbol for the Fourier transform is f(w) or F(w).

3. why the formula for F(w) is called the forwards transform and that for f(t) is called the reverse transform.

Any takers?