# 4.5 Java1486-fun with java, understanding the fast fourier transform  (Page 13/14)

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Figure 10. The numeric output for Case A.
```Case A Real:1.0 0.923 0.707 0.382 0.0 -0.382 -0.707 -0.923 -1.0 -0.923 -0.707 -0.382 0.0 0.382 0.707 0.923imag: 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0```

If you plot the real and imaginary values in Figure 10 , you will see that they match the transform output shown in graphic form in Figure 9 .

## Case B code

The code from the main method for Case B is shown in Listing 6 . Note that the input complex series contains non-zero values in both the real and imaginaryparts.

Listing 6. Case B code.
```System.out.println("\nCase B"); double[]realInB = {0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1};double[] imagInB ={0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1}; double[]realOutB = new double[16];double[] imagOutB = new double[16]; transform.doIt(realInB,imagInB,2.0,realOutB,imagOutB); display(realOutB,imagOutB);```

## Case B in graphical form

Case B is shown in graphical form in Figure 11 .

Figure 11. Case B in graphical form.

## Case B output in numeric form

The output from the code in Listing 6 is shown in Figure 12 .

Figure 12. Case B output in numeric form.
```Case B Real:1.0 0.923 0.707 0.382 0.0 -0.382 -0.707 -0.923 -0.999 -0.923 -0.707 -0.382 0.0 0.382 0.707 0.923imag: -1.0 -0.923 -0.707 -0.382 0.0 0.382 0.707 0.9231.0 0.923 0.707 0.382 0.0 -0.382 -0.707 -0.923```

If you plot the values for the real and imaginary parts from Figure 12 , you will see that they match the real and imaginary output shown in Figure 11 .

## Case C code

The code extracted from the main method for Case C is shown in Listing 7 .

Listing 7. Case C code.
```System.out.println("\nCase C"); double[]realInC = {1.0,0.923,0.707,0.382,0.0,-0.382,-0.707,-0.923,-1.0,-0.923,-0.707,-0.382,0.0, 0.382,0.707,0.923};double[] imagInC ={0.0,-0.382,-0.707,-0.923,-1.0,-0.923, -0.707,-0.382,0.0,0.382,0.707,0.923,1.0,0.923,0.707,0.382}; double[]realOutC = new double[16];double[] imagOutC = new double[16]; transform.doIt(realInC,imagInC,16.0,realOutC,imagOutC); display(realOutC,imagOutC);```

The complex input series for Case C is a little more complicated than that for either of the previous two cases. Note in particular that the input complexseries contains non-zero values in both the real and imaginary parts. In addition, very few of the values in the complex series have a value of zero.

(The values of the complex samples actually describe a cosine curve and a negative sine curve as shown in Figure 13 .)

## The graphic form of Case C

Case C is shown in graphic form in Figure 13 .

Figure 13. The graphic form of Case C.

The Fourier transform is reversible

One of the interesting things to note about Figure 13 is the similarity of Figure 13 and Figure 5 . These two figures illustrate the reversible nature of the Fourier transform.

If I had used a positive input real value instead of a negative input real value in Figure 5 , the input of Figure 5 would look exactly like the output in Figure 13 , and the output of Figure 5 would look exactly like the input of Figure 13 .

With that as a hint, you should now be able to figure out how I used a mouse and drew the perfect sine and cosine curves in Figure 13 . In fact, I didn't draw them at all. Rather, I used my mouse and drew the output, andthe applet gave me the corresponding input automatically.

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