# Determine which of the following sinusoids are periodic and compute their fundamental period. Determine which of the following sinusoids are periodic and compute their fundamental period.  by
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A signal is periodic with period ‘N’ , if and if is a ratio of integers (rational).

N is the time period.

(a) Consider the signal. The value of is, Consider the expression for . …… (1)

Here, is ratio of integers.

Hence, the signal is periodic.

From equation (1), Therefore, the signal has fundamental period .

(b)

Consider the signal. The value of is, Consider the expression for . …… (2)

Here, is ratio of integers.

Hence, the signal is periodic.

From equation (2),

N = 7

Therefore, the signal has fundamental period .

(c) Consider the signal. The value of is, Consider the expression for . …… (3)

Here, is ratio of integers.

Hence, the signal is periodic.

From equation (3),

N = 2

Therefore, the signal has fundamental period .

(d) Consider the signal. The value of is, Consider the expression for . Here, is not rational.

Hence, the signal is not -periodic.

(e) Consider the signal. The value of is, Consider the expression for .  …… (4)

Here, is ratio of integers.

Hence, the signal is periodic.

From equation (4),

N = 10.

Therefore, the signal has fundamental period .

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