MATLAB: Trying to take FFT in frequency domain of spatial signal

fftfrequencyspatialwave number

I have a spatial signal and need to do an fft over the frequency domain. I have seen a few different posts on the topic and there are varying approaches, none of which seem to work for me. The data comes from a simulation algorithm that is too long to post so I will just give the vector it outputs that I'm trying to transform (sorry in advance for the long vector)
if true
    EZ=[ 0
   -0.1059
   -0.1688
   -0.1605
   -0.0773
    0.0592
    0.2104
    0.3347
    0.4035
    0.4113
    0.3752
    0.3226
    0.2738
    0.2291
    0.1696
    0.0728
   -0.0670
   -0.2277
   -0.3688
   -0.4530
   -0.4640
   -0.4103
   -0.3115
   -0.1835
   -0.0338
    0.1284
    0.2829
    0.3977
    0.4416
    0.3993
    0.2840
    0.1396
    0.0311
    0.0169
    0.1100
    0.2558
    0.3543
    0.3274
    0.1851
    0.0316
   -0.0060
    0.1193
    0.3225
    0.4348
    0.3271
    0.0154
   -0.3404
   -0.5530
   -0.5485
   -0.4102
   -0.2888
   -0.2661
   -0.2952
   -0.2663
   -0.1289
    0.0498
    0.1454
    0.0994
   -0.0219
   -0.0918
   -0.0417
    0.0876
    0.2046
    0.2612
    0.2857
    0.3301
    0.3987
    0.4360
    0.3827
    0.2421
    0.0875
    0.0010
    0.0056
    0.0611
    0.1165
    0.1520
    0.1716
    0.1716
    0.1272
    0.0141
   -0.1530
   -0.3088
   -0.3773
   -0.3324
   -0.2213
   -0.1282
   -0.1068
   -0.1418
   -0.1707
   -0.1338
   -0.0035
    0.2050
    0.4153
    0.5069
    0.4096
    0.1897
    0.0057
   -0.0342
    0.0511
    0.1656
    0.2274
    0.2095
    0.1349
    0.0544
    0.0166
    0.0374
    0.0938
    0.1464
    0.1677
    0.1521
    0.1066
    0.0376
   -0.0539
   -0.1603
   -0.2536
   -0.2912
   -0.2428
   -0.1167
    0.0347
    0.1367
    0.1412
    0.0790
    0.0483
    0.1145
    0.2215
    0.2358
    0.0838
   -0.1802
   -0.4329
   -0.5665
   -0.5257
   -0.3260
   -0.0674
    0.1062
    0.1054
   -0.0294
   -0.1501
   -0.1134
    0.1025
    0.3725
    0.5206
    0.4576
    0.2468
    0.0459
   -0.0243
    0.0284
    0.0963
    0.0916
    0.0357
    0.0288
    0.1371
    0.3108
    0.4163
    0.3500
    0.1287
   -0.1263
   -0.2854
   -0.2936
   -0.1778
         0];
Lx = 0.08;         %Total physical Length of cavity
n = length(EZ);
N = Lx*linspace(0,1,n); %total space vector
dx = 5e-4;         %spatial discretization
Fs = 1/dx;         %spatial sampling frequency
k = 2*pi*N/(Lx);   %wavenumber vector (?)
c = 1.4629e+008;   %constant wave speed
f = 2*pi*c./k;     %frequency vector
Y = abs(fft(EZ)/n);
subplot(3,1,1)
plot(N,EZ); 
xlabel('distance');
subplot(3,1,2)
plot(k,Y);
xlabel('wave number');
subplot(3,1,3)
plot(f,Y);
xlabel('frequency');   
end
I don't use all the variables calculated in this version of the code. The fft results look wrong to me. My questions about the results are 1. Is the wave number vector correct? 2. Is the frequency vector correct? The frequency vector seems strange to me. A good thing is that Matlab seems to have plotted it backward for me (arrowing to the right with a data cursor makes it move left) so it appears in the right order. The theoretical values of the frequency fft should be somewhat larger but I don't know how to ensure I have made my axis vectors (k and f) correctly. Thanks in advance for any advice.

Best Answer

Hi Brian
You can see from the plot of x vs EZ that EZ has oscillations of wavelength order .01, so you should be getting k values of 2pi / .01, around 600. Your k vector maxes out at 2pi, so it is off, as you suspected. In this situation, k_max * dx = 2pi, so you need a k vector (with 160 points) that goes from 0 to 2pi / dx = 4000 pi.
After the fft, for plotting purposes it might be better to use fftshift on Y to put k = 0 in the center and use a shifted k vector with positive and negative wave numbers on each side, -2000 pi < k < 2000 pi.
Also your frequency calculation doesn't agree with omega = 2 pi f = c k. f and k are proportional, not inverses of each other.
Related Question