00:01
This question says that determine whether or not each of the following signals is periodic.
00:06
If the signal is periodic, determine its fundamental period.
00:11
So let's start to solve this problem.
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In part a, we have xt is equal to 3.
00:19
Cos 40 plus pi over 3.
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We know a cosine function is always a periodic signal, hence xt is a periodic signal.
00:31
Here coefficient of t is the fundamental frequency of this periodic signal.
00:39
Fundamental frequency is equal to 4.
00:41
And we know fundamental frequency is equal to 2 pi over t, 2 pi over t is equal to 4.
00:48
From this we obtain time period t is equal to pi over 2.
00:56
So here this is the time period of this signal xt.
01:02
That means we have xt plus pi over 2 is equal to.
01:06
To x t in part b we have a discrete signal x n for this cosine discrete signal we have omega not is equals to pi over four for this signal we have omega not is equal to pi over it and for this signal we have omega not is equal to pi over two suppose that n1 is the time period of this signal.
01:41
Then n1 is given by n1 is equal to 2 pi over omega not into n.
01:47
N1 is equal to 2 pi over pi over 4 into n.
01:56
N1 is equal to 8 n.
02:00
Therefore small n equals to 1 capital n1 becomes an integer.
02:07
That means since this is a periodic signal with time period n1 is equal to 8.
02:18
Next, suppose time period of this signal is equal to n2.
02:22
So n2 is given by 2 pi over omega not into end.
02:30
N2 is equal to 2 pi over pi over 8 into n.
02:37
N2 is equal to 16 into n.
02:40
Here for small n is equal to 1 capital n2 becomes an integer.
02:48
That means time period of this signal is equal to 16...