# Carr and Madan Fourier Transform

I am bit confused by Carr and Madan's paper. In it the authors write that the Fourier transform $c_T(k)$ is defined by

\begin{align} \psi_T(v) = \int_{ - \infty}^{\infty} e^{ivk} c_T(k)dk \end{align}

Yet traditionally it is know that the Fourier Transform formula is \begin{align} X( \omega) = \int_{- \infty}^{\infty} x(t) e^{ - i \omega t} dt \end{align}

The negative being the difference between the two.

• as has been said, it's just a convention that varies from field to field. I present various different approaches and show how they agree, in my book More Mathematical Finance. Mar 27 '17 at 5:18