# What's the physical meaning of the Fourier transform of magnetic flux density?

I have here below the distribution of the magnetic flux density $B$ across a 1 pole pitch in the airgap of a synchronous machine. The horizontal axis represents the distance along the arc length formed by a pole pitch across the airgap. If I take the Fourier Transform of this flux density,how should I interpret the results? I am used to taking Fourier Transform with respect to time and not with respect to spatial data that I have here.

Thanks a lot...

Update

I think it makes sense instead to use the Fourier Transform on a complete cycle (i.e. not the half cycle shown up) to look at the harmonics that we have in the magnetic flux density. This is what I get: I guess from the Fourier Transform, this is the only information that is relevant.

• I think that you must have some reason why to use FT prior to using it. FT makes sense only if the quantity is described by differential equation with harmonics as solutions (e.g. differential equation of oscillator)... – Pygmalion Apr 17 '12 at 17:56
• What if I want to look at the harmonic contents? – yCalleecharan Apr 17 '12 at 17:59
• That person who has down-voted me should really explain with reason why he/she has done that...and not just leave a negative vote. Be constructive and brave! – yCalleecharan Apr 17 '12 at 18:01
• Is that a experimentally measured value? – Xiang Apr 17 '12 at 18:02
• Of course you can look at harmonic contents, but what do they mean? IMHO you should know that before making FT... – Pygmalion Apr 17 '12 at 18:02

A fourier transform over spatial data gives a spectrum of spatial frequencies. Where a transform of temporal data gives the amplitude versus cycles per second, spatial frequency has units of cycles per meter (or whatever length unit).

Since I don't see any relevant answers, let me try with this one:

Only you who have intimate knowledge of the problem (experimental setup etc.) could guess, what FT results mean (if anything). Note: because it is symmetric and resembles cosine function, it isn't neccessary a FT. ANY function can be Fourier transformed, this is just matematical operation, like, let's say, multiplying.

My experimental guess would be, that you have exponential falls at the ends and constant value in the middle.

• Providing FT data was helpful. But I really do not see anything significant here. Low "frequencies" just describe the general shape (cosine-type shape). Possible high "frequencies" could be significant, but there is nothing. I'd stick with exponential fall together with a constant. – Pygmalion Apr 18 '12 at 15:09
• Update: If resolution would be higher (larger number of data for FT) maybe some peak at high "frequencies" would distinguish itself. As it is, all high-frequency contribution seem to be noise. But don't take my comments for granted, I did used FT on several completely different problems but it was always time-dependent. – Pygmalion Apr 18 '12 at 15:18
• And by the way "frequency" in your case means how often some value oscillates in space - you know, like wave vector $k$ in $\psi = A \sin(k x - \omega t)$. Which makes me wondering - would you in your experiment expect some kind of standing waves? – Pygmalion Apr 18 '12 at 15:39
• @ Pygmalion Thanks. The flux density distribution I've shown is in the airgap of a synchronous generator. The airgap is the thin air region between the rotating rotor and the stationary armature/stator. I think it's traveling wave as the wave pattern follow the rotor as it moves. – yCalleecharan Apr 18 '12 at 19:27
• @yCalleecharan If so, then the idea is that you should have higher harmonics, i.e. $k_1 = 0.25$, $k_2 = 0.5$, $k_n = n \times k_1$, but the resolution is too small to draw such conclusions. – Pygmalion Apr 18 '12 at 19:31