Question

(Fourier Transform) I'm having trouble understanding why when, coming across a variety of different formulas for the Fourier Transform and its inverse (Sine, Cosine, Complex, etc)-some of the formulas have a coefficient that is a square root, and others do not, but otherwise the formulas are identical. Why is this? Why do some have something like \[\sqrt{\frac{2}{\pi}}\] or \[ \frac{1}{\sqrt{2\pi}} \] and others do not?

Answer 1

@texaschic101

Answer 2

\[\frac1{\sqrt{2\pi}}=\frac{\sqrt{2}}{2\sqrt{\pi}}=\frac12 \sqrt{\frac{2}{\pi}}\]

are some applications doubled? how does the 1/2 affect the situation?

not sure since im not proficient at FS but its a thought

Answer 3

No, I guess I wasn't clear, I mean those coefficients are not square-rooted in other formula that are virtually identical otherwise, and I see both versions often.

Answer 4

@wio

Answer 5

I'm not sure. I guess I'd need more context.

Answer 6

I think I'll just reopen this with a more clear prompt later on, but thanks nonetheless