Show that the complex exponential sequence x [ n ] = ejflun is periodic only if 00/27T is a rational number. By Eq. (1.9), x [ n] will be periodic if or Equation ( 1. 79) holds only if 0 0 N = m 27T'...

Show that the complex exponential sequence

x [ n ]
=
ejflun

is periodic only if 00/27T is a rational number.

By Eq. (1.9),
x [ n]
will be periodic if

or

Equation (
1.79) holds only if

0
0
N= m 27T'
m= positive integer

(1.79)

or

no
m

- = - = rational number

271'&
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