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