The following example reinforces the discussion of the
DFT matrix in
§
6.12. We can simply create the
DFT matrix in
matlab by
taking the DFT of the identity matrix. Then we show that multiplying
by the DFT matrix is equivalent to the calling the
fft
function in matlab:
>> eye(4)
ans =
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
>> S4 = fft(eye(4))
ans =
1 1 1 1
1 0 - 1i -1 0 + 1i
1 -1 1 -1
1 0 + 1i -1 0 - 1i
>> S4' * S4 % Show that S4' = inverse DFT (times N=4)
ans =
4 0 0 0
0 4 0 0
0 0 4 0
0 0 0 4
>> x = [1; 2; 3; 4]
x =
1
2
3
4
>> fft(x)
ans =
10
-2 + 2i
-2
-2 - 2i
>> S4 * x
ans =
10
-2 + 2i
-2
-2 - 2i
Previous Section:
DFT Bin Response
