Periodic / Non-Periodic Functions

CONTINUOUS TIME (CT) For a function to be continuous in discrete time, it must satisfy $ a(x+T) = a(x) $ for any T greater than zero. Furthermore, any continuous time function that does not satisfy the pre-mentioned condition can be deemed non-periodic.

Ex1: y(t) = cos(t) is periodic

Example 1 is periodic since it satisfies the requirement a(x+T) = a(x) for T>0.

Ex2: x(t) = e^3t is non-periodic

Example 2 is non-periodic because it does not satisfy the requirement a(x+T) = a(x) for T>0.

DISCRETE TIME (DT) For a function to be continuous in discrete time, it must satisfy $ a[n+T] = a[n] $ for an integer T. If these conditions are not met, then it is deemed non-periodic. Furthermore, both sin and cosine are non-periodic in discrete time.

Ex1: y[n] = 1 is continuous

Ex2: x[n] = cos[n] is non-periodic

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