Fourier transform as the integral of a parameter multiplied by an homogeneous wave
given your definition, and the definition of the Fourier transfer:
yes. That is literally the definition:
$$\int_{\mathbb R} s(x) e^{i2\pi f x} \mathrm dx$$
By comparison, with $k= 2\pi f$, you get the Fourier transform. Every book uses that definition, so you'll find this &quot;interpretation&quot; in every book that introduces the Fourier transform. (This really feels like exactly the same $k$-space / location transform I learned in my first solid state physics lecture, so I assume every modern solid state course for physicists does pretty much that, but more in-depth.)