Physical meaning of a fourier transform?

1. Feb 22, 2008

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.

2. Feb 22, 2008

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.

3. Feb 22, 2008

Hurkyl

Staff Emeritus
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.

4. Feb 22, 2008

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.

5. Feb 22, 2008

Staff: Mentor

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

6. Feb 22, 2008

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.

7. Feb 22, 2008

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:

Nonetheless, my mind is at rest :)