The Fourier-Bros-Iagolnitzer transform is given by the functional
$$ \mathcal {F}\{f(t)\}=(2\pi )^{{-n/2}}\int _{{{{\mathbf R}}^{n}}}f(x)e^{{-a|x-y|^2/2}}e^{ix\cdot t},dx.$$
I applied this on a set of $L_2$ functions, which are Fourier series in the form of
$$f(t)=(2i+2)e^{5it}$$
However, the orientation of the wave peak that is generated by the transform occurred orthogonally by 90 degrees to the wave-train of $f(t)$. See image below.
By the form of the functional , I cannot think of any way to change it so that the large wave peak that arises after a series of steps occurs in the same wave-directions as the surrounding waves.
Does anyone have an idea if this is even possible?
Thanks
