x(n) = z^n

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Let x(n) = z^n where z = A exp(jω). If x(n) is formed by sampling the continuous signal x(t) = exp(st) at integer multiples of a period T, then we see that z = exp(sT). x(n) forms a spiral in the z-plane. A < 1 : spiral in A > 1 : spiral out A = 1 : no spiral (circle) ω < 0 : spiral clockwise ω > 0 : spiral counter-clockwise ω = 0 : no spiral (trace real axis) Notice that a frequency of ω is indistinguishable from that of ω+2π. The discrete-ness in the time domain causes the frequency domain to be periodic. This is known as aliasing.