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150 Chapter 5 THE DISCRETE FOURIER TRANSFORM
or
˜x(n) =
∞∑
r=−∞
x(n − rN) =···+ x(n + N)+x(n)+x(n − N)+··· (5.16)
which means that when we sample X(z) onthe unit circle, we obtain a
periodic sequence in the time domain. This sequence is a linear combination
of the original x(n) and its infinite replicas, each shifted by multiples
of ±N. This is illustrated in Example 5.5. From (5.16), we observe that if
x(n) =0for n