How to solve the Fast Fourier transform?

Fourier transform! What is the correct formula?

• I m having trouble in determining that what is the correct formula for the fourier transform. In the book "Advance Engineering Mathematics" by erwin kreyszig, the formula used for the fourier transform is: ((1/2*pi)^(1/2))*integral from - inf. to + inf. of (f(x)*e^(-jwx)).dx whereas all over the net i m not able to find this formula. the formula for Fourier transform available on the net is simply: integral from - inf. to + inf. of (f(x)*e^(-jwx)).dx Both these formulae are not equal. What is the correct formula and whats your reason to say it correct? Please give logical answers... thanks..

• Answer:

  At first, I thought the top formula (with the √(1/2π) ) was using that factor as a normalization factor. I found this article (well referenced) on Wiki: Check near the bottom ("Other Conventions" and "Tables of Important..."_) http://en.wikipedia.org/wiki/Fourier_transform But even that doesn't fully explain the difference. It may be that the top formula is misprinted. How are the two frequencies (listed both as 'w') defined in the Advanced Engineering... text, and elsewhere? That may be the problem. If one is defining the frequency in radians/second versus Hz, then there will be a difference in how the transform is computed. .