From Cozzi-Protti-Ruaro - Elementi di Chimica Analitica Strumentale, page 244:
However, since the IR sources are of the continuous type, i.e. they emit over the entire spectral range, the interferogram is described by the equation
$$I(\delta) = \int^{+\infty}_{-\infty} B(\nu) \cos(2\pi\delta\nu) \,d\nu$$
where
- $I$ = wave intensity
- $\delta$ = Michelson interferometer moving mirror offset (just like a phase constant)
- $B$ = maximum intensity
- $\nu$ = wave frequency
To obtain the inverse function, i.e. the intensity as a function of $\nu$, this equation is reworked with the Fourier transform
$$B(\nu) = \int^{+\infty}_{-\infty} I(\delta) \cos(\delta\nu) \,d\delta$$
But when this integral does not converge: the test can be done in the case of a single frequency. Could it be that the book has given a wrong formula?