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Properties of the Discrete Fourier Transform 167
10
8
Original sequence
x(n)
6
4
2
0
0 1 2 3 4 5 6 7 8 9 10
n
Circularly folded sequence
10
x(-n mod 11)
8
6
4
2
0
0 1 2 3 4 5 6 7 8 9 10
n
FIGURE 5.12 Circular folding in Example 5.9a
50
Real{DFT[x(n)]}
20
Imag{DFT[x(n)]}
40
30
20
10
0
10
−10
0
0 5 10
k
−20
0 5 10
k
50
Real{DFT[x((-n))11]}
20
Imag{DFT[x((-n))11]}
40
30
20
10
0
10
−10
0
0 5 10
−20
0 5 10
k
k
FIGURE 5.13 Circular folding property in Example 5.9b
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