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Consider a signal x(t) = 4 cos (2t/3) + 8 sin (0.5t) + 7 sin (t/3 – π/6)
Calculate the fundamental period.
- a)6π seconds
- b)2π seconds
- c)12π seconds
- d)π seconds
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Consider a signal x(t) = 4 cos (2t/3) + 8 sin (0.5t) + 7 sin (t/3 &nda...
To find the amplitude and frequency components of the given signal x(t), we can break it down into its cosine and sine components separately:
x(t) = 4 cos (2t/3) + 8 sin (0.5t) + 7 sin (t/3)
The amplitude of a cosine or sine function can be found by taking the coefficient in front of it.
For the cosine component:
Amplitude = 4
For the sine components:
Amplitude = 8 for sin (0.5t)
Amplitude = 7 for sin (t/3)
The frequency of a cosine or sine function can be found by taking the coefficient of t inside the function and dividing it by 2π.
For the cosine component:
Frequency = 2/3π
For the sine components:
Frequency = 0.5/2π = 1/4π for sin (0.5t)
Frequency = 1/3π for sin (t/3)
Therefore, the amplitude and frequency components of the given signal x(t) are as follows:
Amplitude:
Cosine component = 4
Sine component 1 = 8
Sine component 2 = 7
Frequency:
Cosine component = 2/3π
Sine component 1 = 1/4π
Sine component 2 = 1/3π
x(t) = 4 cos (2t/3) + 8 sin (0.5t) + 7 sin (t/3)
The amplitude of a cosine or sine function can be found by taking the coefficient in front of it.
For the cosine component:
Amplitude = 4
For the sine components:
Amplitude = 8 for sin (0.5t)
Amplitude = 7 for sin (t/3)
The frequency of a cosine or sine function can be found by taking the coefficient of t inside the function and dividing it by 2π.
For the cosine component:
Frequency = 2/3π
For the sine components:
Frequency = 0.5/2π = 1/4π for sin (0.5t)
Frequency = 1/3π for sin (t/3)
Therefore, the amplitude and frequency components of the given signal x(t) are as follows:
Amplitude:
Cosine component = 4
Sine component 1 = 8
Sine component 2 = 7
Frequency:
Cosine component = 2/3π
Sine component 1 = 1/4π
Sine component 2 = 1/3π
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Community Answer
Consider a signal x(t) = 4 cos (2t/3) + 8 sin (0.5t) + 7 sin (t/3 &nda...
Concept:
Continious time signal x(t) is given as,
x(t) = x1(t) + x2(t)
Then, Time period of x(t) is (N) = LCM (T1, T2,)
Time period of x1(t) is Given as:
T1 = 2π / ω01
Time period of x2(t) is Given as:
T2 = 2π / ω02
Calculation:
Given:
T1 = 2π / 2/3 = 3π
T2 = 2π / .5 = 4π
T3 = 2π / 13 = 6π
Time period = L.C.M. (T1, T2, T3)
= L.C.M. (3π, 4π, 6π)
= 12π
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Consider a signal x(t) = 4 cos (2t/3) + 8 sin (0.5t) + 7 sin (t/3 – π/6)Calculate the fundamental period.a)6π secondsb)2π secondsc)12π secondsd)π secondsCorrect answer is option 'C'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2026 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Consider a signal x(t) = 4 cos (2t/3) + 8 sin (0.5t) + 7 sin (t/3 – π/6)Calculate the fundamental period.a)6π secondsb)2π secondsc)12π secondsd)π secondsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a signal x(t) = 4 cos (2t/3) + 8 sin (0.5t) + 7 sin (t/3 – π/6)Calculate the fundamental period.a)6π secondsb)2π secondsc)12π secondsd)π secondsCorrect answer is option 'C'. Can you explain this answer?.
Consider a signal x(t) = 4 cos (2t/3) + 8 sin (0.5t) + 7 sin (t/3 – π/6)Calculate the fundamental period.a)6π secondsb)2π secondsc)12π secondsd)π secondsCorrect answer is option 'C'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2026 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Consider a signal x(t) = 4 cos (2t/3) + 8 sin (0.5t) + 7 sin (t/3 – π/6)Calculate the fundamental period.a)6π secondsb)2π secondsc)12π secondsd)π secondsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a signal x(t) = 4 cos (2t/3) + 8 sin (0.5t) + 7 sin (t/3 – π/6)Calculate the fundamental period.a)6π secondsb)2π secondsc)12π secondsd)π secondsCorrect answer is option 'C'. Can you explain this answer?.
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