I've noticed that many journal articles (in optics) use the phrase "Fourier frequency" to describe, well, the frequency of something.
To compare with previous sensitivity curves of a single LISA
Michelson interferometer, we construct the SNRs as a function of
Fourier frequency for sinusoidal waves from sources uniformly
distributed on the celestial sphere.
This phrase seems redundant to me. Does the adjective "Fourier" add anything? Is it trying to make a distinction of audio frequencies from optical frequencies? Or temporal frequencies from spatial frequencies?
Best Answer
The term Fourier frequency most usually denotes the frequency of one of several components of a function which may or may not be periodic. Take, for example, a gaussian pulse, which you can decompose as a "sum" (integral) of different periodic waves, $\cos(\omega t)$, with weights that vary with $\omega$: $$e^{-{t^2}/{2T^2}}=\int_{-\infty}^\infty \frac{e^{-T^2\omega^2/2}}{\sqrt{2\pi}}\cos(\omega t)d\omega.$$ In this context it's quite appropriate to call $\omega$ a Fourier frequency since it's not the frequency of the function under consideration, but only of part of it in a certain decomposition. The general techniques for doing this are Fourier transforms and series, depending on what type of function you are dealing with.