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Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?
- a)8
- b)12
- c)18
- d)24
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Define the fundamental period of the following signal x[n] = exp(2pi*j...
The first signal, will repeat itself after 3 cycles. The second will repeat itself after 8 cycles. Thus, both of them together will repeat themselves only after LCM(8,3) = 24 cycles.
Most Upvoted Answer
Define the fundamental period of the following signal x[n] = exp(2pi*j...
Fundamental Period of Signal x[n]
The fundamental period of a discrete-time signal is defined as the smallest positive integer value of N for which the signal repeats itself after N samples. In other words, if we shift the signal by N samples, the resulting signal is identical to the original signal.
Signal Definition
The given signal is x[n] = exp(2pi*j*n/3) * exp(3*pi*j*n/4) where j is the imaginary unit and n is an integer.
Analysis
To find the fundamental period of the signal, we need to determine the value of N such that x[n] = x[n+N] for all values of n. That is,
exp(2pi*j*n/3) * exp(3*pi*j*n/4) = exp(2pi*j*(n+N)/3) * exp(3*pi*j*(n+N)/4)
We can simplify this equation by canceling out the common factors and using the fact that exp(2pi*j) = 1. That is,
exp(3*pi*j*n/4) = exp(3*pi*j*(n+N)/4)
Taking the natural logarithm of both sides, we get
ln(exp(3*pi*j*n/4)) = ln(exp(3*pi*j*(n+N)/4))
3*pi*j*n/4 = 3*pi*j*(n+N)/4 + 2*k*pi*j where k is an integer
Simplifying this equation, we get
N = 12
Therefore, the fundamental period of the given signal is 12.
The fundamental period of a discrete-time signal is defined as the smallest positive integer value of N for which the signal repeats itself after N samples. In other words, if we shift the signal by N samples, the resulting signal is identical to the original signal.
Signal Definition
The given signal is x[n] = exp(2pi*j*n/3) * exp(3*pi*j*n/4) where j is the imaginary unit and n is an integer.
Analysis
To find the fundamental period of the signal, we need to determine the value of N such that x[n] = x[n+N] for all values of n. That is,
exp(2pi*j*n/3) * exp(3*pi*j*n/4) = exp(2pi*j*(n+N)/3) * exp(3*pi*j*(n+N)/4)
We can simplify this equation by canceling out the common factors and using the fact that exp(2pi*j) = 1. That is,
exp(3*pi*j*n/4) = exp(3*pi*j*(n+N)/4)
Taking the natural logarithm of both sides, we get
ln(exp(3*pi*j*n/4)) = ln(exp(3*pi*j*(n+N)/4))
3*pi*j*n/4 = 3*pi*j*(n+N)/4 + 2*k*pi*j where k is an integer
Simplifying this equation, we get
N = 12
Therefore, the fundamental period of the given signal is 12.
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Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?a)8b)12c)18d)24Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?a)8b)12c)18d)24Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?a)8b)12c)18d)24Correct answer is option 'D'. Can you explain this answer?.
Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?a)8b)12c)18d)24Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?a)8b)12c)18d)24Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?a)8b)12c)18d)24Correct answer is option 'D'. Can you explain this answer?.
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