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The discrete-time signal x (n) = (-1)n is periodic with fundamental period
- a)6
- b)4
- c)2
- d)0
Correct answer is option 'C'. Can you explain this answer?
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The discrete-time signal x (n) = (-1)nis periodic with fundamental per...
Explanation: Period of the signal refers to the instant of time at which the signal repeats itself and for this Period =2 of the given discrete time signal.
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The discrete-time signal x (n) = (-1)nis periodic with fundamental per...
Explanation:
The given discrete-time signal is x(n) = (-1)n. To determine the fundamental period of this signal, we need to find the smallest positive integer value of N such that x(n) = x(n+N) for all values of n.
Periodicity of the signal:
Let's check the signal for different values of n to determine its periodicity:
For n = 0, x(0) = (-1)^0 = 1
For n = 1, x(1) = (-1)^1 = -1
For n = 2, x(2) = (-1)^2 = 1
For n = 3, x(3) = (-1)^3 = -1
For n = 4, x(4) = (-1)^4 = 1
From the above values, we can observe that the signal x(n) alternates between 1 and -1 as n increases. This means that the signal repeats itself every 2 samples.
Fundamental Period:
The fundamental period of a periodic signal is the smallest positive integer value of N for which the signal repeats itself. In this case, the signal x(n) repeats itself every 2 samples.
Therefore, the fundamental period of the given signal x(n) = (-1)n is 2.
Answer:
The correct answer is option C) 2.
The given discrete-time signal is x(n) = (-1)n. To determine the fundamental period of this signal, we need to find the smallest positive integer value of N such that x(n) = x(n+N) for all values of n.
Periodicity of the signal:
Let's check the signal for different values of n to determine its periodicity:
For n = 0, x(0) = (-1)^0 = 1
For n = 1, x(1) = (-1)^1 = -1
For n = 2, x(2) = (-1)^2 = 1
For n = 3, x(3) = (-1)^3 = -1
For n = 4, x(4) = (-1)^4 = 1
From the above values, we can observe that the signal x(n) alternates between 1 and -1 as n increases. This means that the signal repeats itself every 2 samples.
Fundamental Period:
The fundamental period of a periodic signal is the smallest positive integer value of N for which the signal repeats itself. In this case, the signal x(n) repeats itself every 2 samples.
Therefore, the fundamental period of the given signal x(n) = (-1)n is 2.
Answer:
The correct answer is option C) 2.
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