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 
.
If you found this answer helpful, please upvote and share with other students in your network.
