PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

502 Practical MATLAB® Applications for Engineers

>> f _ 3by3 = magic(3) % part(f)

f_3by3 =

8 1 6

3 5 7

4 9 2

>> DFT _ f _ 3by3 = (fft(f _ 3by3))’

DFT _ f _ 3by3 =

15.0000 4.5000 - 0.8660i 4.5000 + 0.8660i

15.0000 -6.0000 - 3.4641i -6.0000 + 3.4641i

15.0000 1.5000 + 4.3301i 1.5000 - 4.3301i

>> %Note that the results obtained in part(g) are not equal to part(f)

>> f _ trans _ 3by3 = (magic(3))’ % part(g)

f_trans_3by3 =

8 3 4

1 5 9

6 7 2

>> DFT _ f _ trans _ 3by3 = (fft(f _ trans _ 3by3))’ % part(h)

DFT _ f _ trans _ 3by3 =

15.0000 4.5000 - 4.3301i 4.5000 + 4.3301i

15.0000 -3.0000 - 1.7321i -3.0000 + 1.7321i

15.0000 -1.5000 + 6.0622i -1.5000 - 6.0622i

>> DFT _ f _ trans _ 3by3 = (fft2(f _ trans _ 3by3))’

DFT _ f _ trans _ 3by3 =

45.0000 0 0

0 13.5000 - 7.7942i 0 + 5.1962i

0 0 - 5.1962i 13.5000 + 7.7942i

>> DFT _ f _ 3by3 = (fft2(f _ 3by3))’

DFT _ f _ 3by3 =

45.0000 0 - 0.0000i 0 + 0.0000i

0 13.5000 - 7.7942i 0.0000 - 5.1962i

0 0.0000 + 5.1962i 13.5000 + 7.7942i

R.5.138 The command fft is used to evaluate the correlation function, which is used in
signal detection and estimation, in applications such as radar and sonar.
The autocorrelation of f 1 (n) is defi ned as:

Rs fnfn s s

n

11 ()
 1 ( ) ( 1 ) 

 



∑ over the range        

where s is referred to as the scanning or searching parameter. Observe that the
autocorrelation is very similar to the convolution. Recall that the convolution is
given by

fs fs fnfs n

n

12 ()⊗ ()
∑ 12 ( ) ( )