Why Normalization Factors in Fourier Transform Pairs?

[fisico30]

hello forum,
a question about normalization factors in the Fourier transform pairs:

why is it that a factor 1/2*pi in only one, or 1/sqrt(2pi) in both, or no factor (in the case the complex basis functions have argument 2*pi*f) need to be in front of the Fourier transform pair?

I understand normalization and its importance in the dot product calculation of coefficients.
Sines, cosines, and complex exponentials have normalization factors equal to 1/sqrt(pi)...
in order to get modulus one...


thanks
fisico30

 

[malawi_glenn]

it is there for normalization as you said, and there exists several conventions which works.

 

[fisico30]

so,

exp (i*w*t) and exp (i*2*pi*f*t) don't have the same normalization factors? Why?

 

[malawi_glenn]

since you have 2pi already in the exponential