I had a hard time finding examples of complex arrays[],  multidimensional complex arrays[][], single dimension and multidimensional ffts.  Attached is the code that i came up to work.  It is not clean and does declare some variables that are not used, but it does work.  Also, I am neither a Java or Processing expert, so feel free to improve .  I used an image called square30.jpeg.  You can find this and others on the web.

How to use:

1.      Load Apache Commons Math Library.  There are numerous threads on how to do this in the forum. Load this in your Processing Libraries.  You need commons-math-2.2.  See threads.  When you save in library,  remove dashes and periods from library and file names.

2.      Must use an image that is a power of 2.  If not, you need to pad the image to that size.

3.      Image must be in local processing project folder.

Good luck!

2. import org.apache.commons.math.stat.clustering.*;
3. import org.apache.commons.math.stat.descriptive.summary.*;
4. import org.apache.commons.math.analysis.polynomials.*;
5. import org.apache.commons.math.analysis.integration.*;
6. import org.apache.commons.math.stat.inference.*;
7. import org.apache.commons.math.stat.*;
8. import org.apache.commons.math.complex.*;
9. import org.apache.commons.math.dfp.*;
10. import org.apache.commons.math.stat.descriptive.*;
11. import org.apache.commons.math.ode.jacobians.*;
12. import org.apache.commons.math.special.*;
13. import org.apache.commons.math.stat.descriptive.rank.*;
14. import org.apache.commons.math.*;
15. import org.apache.commons.math.exception.*;
16. import org.apache.commons.math.stat.correlation.*;
17. import org.apache.commons.math.stat.regression.*;
18. import org.apache.commons.math.util.*;
19. import org.apache.commons.math.analysis.solvers.*;
20. import org.apache.commons.math.optimization.general.*;
21. import org.apache.commons.math.analysis.interpolation.*;
22. import org.apache.commons.math.analysis.*;
23. import org.apache.commons.math.stat.descriptive.moment.*;
24. import org.apache.commons.math.ode.sampling.*;
25. import org.apache.commons.math.optimization.univariate.*;
26. import org.apache.commons.math.estimation.*;
27. import org.apache.commons.math.geometry.*;
28. import org.apache.commons.math.fraction.*;
29. import org.apache.commons.math.ode.events.*;
30. import org.apache.commons.math.genetics.*;
31. import org.apache.commons.math.ode.*;
32. import org.apache.commons.math.random.*;
33. import org.apache.commons.math.transform.*;
34. import org.apache.commons.math.optimization.direct.*;
35. import org.apache.commons.math.ode.nonstiff.*;
36. import org.apache.commons.math.linear.*;
37. import org.apache.commons.math.optimization.*;
38. import org.apache.commons.math.exception.util.*;
39. import org.apache.commons.math.distribution.*;
40. import org.apache.commons.math.stat.ranking.*;
41. import org.apache.commons.math.optimization.fitting.*;
42. 
    
43. /*******************************************************************************************************
44. Example of Complex Array,  Multi-Dimensional Complex Array,  Single dimensional and Multi dimensional
45. fast fourier transform using the Apache Commons Math Library
46. By john.d.engnr Feb. 2012
47. Have fun!!!
48. *******************************************************************************************************/
49. 
    
50. PImage img;
51. float rr,ri;
52. int rs;
53. int row,col, rw,cl,pos;
54. double pix;
55. 
    
56. FastFourierTransformer transformer = new FastFourierTransformer();
57. FastFourierTransformer trans2 = new FastFourierTransformer();
58. Complex result[];
59. Complex realresult[][];
60. 
    
61. 
    
62. void setup() {
63.   
64.   size(1024, 256);
65.   noFill();
66.   stroke(255);
67.   frameRate(30);
68.   img = loadImage("square30.jpg");
69.   col = img.width;
70.   row = img.height;
71.   double [] c = new double[col];
72.   Complex [][]realresult = new Complex[row][col];
73.   Complex [][]cc = new Complex[row][col];
74.   Complex z = new Complex(0.0,0.0);
75.   
76.   set(0,0,img);
77.  
78.   img.loadPixels();
79.  
80.    
81.  
82.   for( rw =0; rw < row; rw++)
83.     {  
84.     for( cl =0; cl < col; cl++)
85.         {
86.         pos = (rw*col) + cl;
87.         c[cl] = red(img.pixels[pos]);
88.         }
89.        
90.        result = transformer.transform(c);
91.       
92.        for ( cl = 0; cl < col; cl++)
93.        {
94.          pos = (rw*col) + cl;
95.          rr =(float)result[cl].getReal();
96.          ri = (float)result[cl].getImaginary();
97.          rs = (int)sqrt(sq(rr) + sq(ri));
98.          img.pixels[pos] =  color(rs);
99.     }      
100.       
101.   }
102. 
     
103. 
     
104.   
105.   img.updatePixels();
106.   
107.   set(256,0,img);
108.   
109.   /*****************************************************************************
110.   reload image for multidimentional fft -- array has to be complex.  
111.   Must reload img.pixels (single dimentional real) to multi dimentional complex)
112.   ******************************************************************************/
113.   
114.   img = loadImage("square30.jpg");
115.   img.loadPixels();
116.   
117.   
118.   for( rw =0; rw < row; rw++)
119.     {  
120.     for( cl =0; cl < col; cl++)
121.         {
122.         pos = (rw*col) + cl;
123.         pix = (double) red(img.pixels[pos]); //load pixels from single dimension to two dimensional array
124.         cc[rw][cl] =  new Complex(pix,0.00D);
125.         }
126.     }
127.    
128.   realresult = (Complex[][])trans2.mdfft(cc,true);
129.     
130.    for ( rw = 0; rw < row; rw++)
131.      {
132.        for ( cl = 0; cl < col; cl++)
133.        {
134.          pos = (rw*col) + cl;
135.          rr =(float)realresult[rw][cl].getReal();
136.          ri = (float)realresult[rw][cl].getImaginary();
137.          rs = (int)sqrt(sq(rr) + sq(ri));
138.          img.pixels[pos] =  color(rs*20);// multiply color by 20 to intensify white
139.          }
140.     }      
141.     img.updatePixels();
142.     set(512,0,img);
143. /************************************************************************************************
144. Convert Fourier transform from frequency domain back to time domain
145. ************************************************************************************************/
146. 
     
147.     cc = (Complex[][])trans2.mdfft(realresult,false);
148.     
149.     for ( rw = 0; rw < row; rw++)
150.       {
151.        for ( cl = 0; cl < col; cl++)
152.        {
153.          pos = (rw*col) + cl;
154.          rr =(float)cc[rw][cl].getReal();
155.          ri = (float)cc[rw][cl].getImaginary();
156.          rs = (int)sqrt(sq(rr) + sq(ri));
157.          img.pixels[pos] =  color(rs);
158.         
159.        }
160.        }
161.     img.updatePixels();
162.     set(768,0,img);
163. }
164.