Loading DocumentDetermine whether or not the signals below are periodic and, for each signal that is periodic, determine the fundamental period.
1) x(n) = cos(0.125πn)
2) x(n) = cos(0.125πn + 1)
3) x(n) = Re(e12jnπ) + Im(e18jnπ)
4) x(n) = sin(π + 0.2n)
5) x(n) = e16jnπCos(17nπ)
1) x(n) = cos(0.125πn)
Angular Frequency ω=0.125π=8π
For a discrete function to be periodic, there must exist a positive integer N and an integer k that satisfy the following relation:
ωN=2πk → 2πω=Nk(Must be Rational Number)
Hince:
2πω=2π8π=16ππ=161→Nk=161→N=16
So x(n) = cos(0.125πn) is Periodic Function and its period is N=16
