The fundamental period for the given signal x(n) = Reejnπ+

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The fundamental period for the given signal
x(n) = Re e jnπ + Img e jnπ
12 18

1. 72
2. 36
3. 24
4. None of these

Correct Option: A

Given signal, x(n) = Re		e	jnπ		+ Img		e	jnπ
			12					18

x(n) = cos	nπ	+ j sin	nπ
	12		18

Fundamental period of

x₁(n)= N₁ =	2π	m =	2π	· m = 24
x₁(n)= N₁ =	Ω	m =	17	· m = 24
			12

Fundamental period of

x₂(n)= N₂ =	2π	m =	2π	· m = 36
x₂(n)= N₂ =	Ω	m =	17	· m = 36
			18

Fundamental period of the signal x[n]. Greatest common mean (GCM) of x₁[n] and x₂[n]
GCM of 24 and 36 = 72.