A cochlea? Yes, that does occur naturally, and it does work to allow us to hear different frequencies of sound...

So, now the next question is, could we prove that a cochlea implements a Fourier Transformation? Note that this Fourier Transform isn't applicable to all frequencies, that is, our ears cannot hear vibrations beyond a certain high pitch, so if a Fourier Transformation could be proved, we could almost think of this as a Fourier Transformation inside of a specific range of frequencies...

But anyway, an interesting observation!

We know how it works, and it's a simple version of a Fourier transform. The cochlea has hairs of different lengths that vibrate according to the contribution of the sine wave that corresponds to the resonant frequency of that hair's length. By the time neurons get involved at all, it's already a signal of the frequency domain over time.