# Question on Definition of Fourier Transform

1. Mar 7, 2012

### nickmai123

I have a question, specifically to physics people, on their definition of the Fourier Transform (and its inverse by proxy). I'm an EE and math person, so I've done a lot of analysis of (real/complex) and work with (signal processing) the transform.

In a physics class I'm taking, the professor defined the transform with the negative signs in the forward and reverse kernels flipped; this is against any and all known conventions that I'm aware of. Theoretically, it doesn't make a difference since its a simple substitution, but in practice, it causes really screws things up like using an FFT function built into MATLAB and Mathematica. Also, the tables of transforms and properties are all flipped around.

That is, in the physics class, the forward (and reverse) transforms are as follows:

$$\mathcal{F}\left\{x\left(t\right)\right\}(f) = X\left(f\right) = \int_{-\infty}^{\infty}x\left(t\right)e^{j2\pi f t}dt$$

$$\mathcal{F}^{-1}\left\{X\left(f\right)\right\}(t) = x\left(t\right) = \int_{-\infty}^{\infty}X\left(f\right)e^{-j2\pi f t}df$$

Is there a reason for this? I can't think of a physical situation where defining the transforms as such is more advantageous than the generally accepted formulas.

2. Mar 7, 2012

### mathman

There is no reason. Which has + and which has - in the exponent is purely a matter of convention. You might ask your professor why he switched - it may have been an oversight. You should bring up the possible problems with MATLAB and Mathematica.