Physical meaning of a fourier transform?

[dst]

Are there any "real" examples of a Fourier transform being applied? When we see that something accelerates and then moves we can say its acceleration is being "integrated" to get a velocity, but what meaning does a Fourier transform have? I understand it's used in spectroscopy but I mean "natural" applications only.

 

[rbj]

maybe it's just because i work in signal processing, but the concept of breaking a virtually arbitrary signal into a sum of sinusoids (more specifically e^{i \omega t}) is an extremely useful application and does a good job of representing the physical situation, particularly for Linear, Time-Invariant (LTI) systems.

 

[Hurkyl]

Are there any "real" examples of a Fourier transform being applied?

In every application I know, a Fourier transform is nothing more than a change of basis; it simply allows you to represent the same object in a different way.

 

[Andy Resnick]

The far-field scattering pattern for light is (under certain conditions) the Fourier transform of the aperture. In crystallography and such, the scattering pattern (Laue pattern) is the Fourier transform of the charge distribution within a unit cell.

Fourier transforms are used a lot in optics. It has a very physical application- the optical field at a focal plane is the Fourier transform of the optical field at the opposite pupil plane.

Electrical signal processing is another real-world use: the equalizer on a stereo, or windoze media player. Guitar effects can work via manipulating the frequency content.

 

[Dale]

Are there any "real" examples of a Fourier transform being applied? When we see that something accelerates and then moves we can say its acceleration is being "integrated" to get a velocity, but what meaning does a Fourier transform have? I understand it's used in spectroscopy but I mean "natural" applications only.

In MRI (Magnetic Resonance Imaging) the voltage that is physically induced in the receive coil is the Fourier transform of the tissue magnetization.

 

[FredGarvin]

Along what rbj mentioned, without an FFT, frequency analysis of vibrations on a running jet engine would be impossible. Looking at the frequency domain instead of the time domain is about a factor of 1 bazillion times easier.

 

[dst]

Thanks, good examples. It's hard to visualise what would be meant by such a thing. I was asking especially for cases where it happens automatically, i.e. by nature like:

the optical field at a focal plane is the Fourier transform of the optical field at the opposite pupil plane

the voltage that is physically induced in the receive coil is the Fourier transform of the tissue magnetization

Nonetheless, my mind is at rest :)