Understanding where the constant $2/N$ comes from in Fourier transformation

1. What is the Fourier transform of where is a constant?
2. Why is there a 2pi in Fourier transform?
3. What is N point Fourier transform?
4. Does FFT have to be power of 2?

What is the Fourier transform of where is a constant?

Fourier Transform of Constant Amplitude

Then, the function X(t) is a constant function and it is not absolutely integrable, hence its Fourier transform cannot be found directly. Therefore, the Fourier transform of X(t)=1 is determined through inverse Fourier transform of impulse function [δ(ω)].

Why is there a 2pi in Fourier transform?

The pi-factor is there to insure symmetry between the Fourier transform and its inverse. Without it, the inverse would need a factor of 1/2pi to compensate.

What is N point Fourier transform?

N is the number of points used to calculate the fft, it does not increase physical resolution but adds more point to the spectrum for more visual resolution, N is arbitrary.

Does FFT have to be power of 2?

Sure, you can use a radix-2 FFT to compute FFTs for lengths not a power of 2 (but it is not as efficient as using methods specifically tailored to the factors of the sequence length).