Periodic versus non-periodic functions (hw1, ECE301)

Read the instructor's comments here.

Periodic Function

x(t) is periodic if there exists:

        T > 0   x(t+T) = x(t)

x[n] is periodic if there exists:

        N > 0   x[n+N] = x[n]

Example in DT

       $  y = j^n  $

j^n has a period of 4.

n = 1: y = j n = 2: y = -1 n = 3: y = -j n = 4: y = 1 n = 5: y = j n = 6: y = -1 n = 7: y = -j n = 8: y = 1

Non-Periodic Function

Example in DT

      $  y = cos(n)  $

cos(n+N) = cos(n) for all n. N must be a multiple of 2*pi. 2*pi is not an integer, but N must be an integer in order to be periodic.

Therefore, y = cos(n) is not periodic.