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An absolutely integrable signal x(t) is known to have Laplace transform with only one pole at s = 4 the x(t) is
- a)Left sided signal
- b)Right sided signal
- c)Signal of finite duration
- d)Double sided signal
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
An absolutely integrable signal x(t) is known to have Laplace transfor...
Since the pole is at s = 4 the function is absolutely integrable thus it must contain jω axis
Hence the signal is left sided
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An absolutely integrable signal x(t) is known to have Laplace transfor...
Laplace Transform and Poles
The Laplace transform is a mathematical tool used to analyze signals and systems in the frequency domain. It is particularly useful in solving differential equations and studying the behavior of linear time-invariant (LTI) systems.
The Laplace transform of a signal x(t) is defined as X(s) = ∫[0 to ∞] x(t)e^(-st) dt, where s is a complex variable.
In the Laplace domain, the complex variable s can have different values. The poles of the Laplace transform are the values of s for which the transform becomes infinite. Poles provide important information about the behavior and characteristics of the signal.
Given Information
In this question, we are given that the Laplace transform of the signal x(t) has only one pole at s = 4. This means that the transform X(s) has a term of the form 1/(s - 4).
Explanation
To determine the nature of the signal x(t), we need to analyze the pole at s = 4.
When a pole is located in the left-half of the complex plane (i.e., Re(s) < 0),="" the="" corresponding="" signal="" x(t)="" is="" left-sided.="" this="" means="" that="" the="" signal="" is="" non-zero="" only="" for="" t="" />< />
When a pole is located in the right-half of the complex plane (i.e., Re(s) > 0), the corresponding signal x(t) is right-sided. This means that the signal is non-zero only for t > 0.
In this case, the pole is located at s = 4, which has a positive real part. Therefore, the signal x(t) is right-sided.
Conclusion
Based on the given information, we can conclude that the signal x(t) is a right-sided signal. Therefore, the correct answer is option 'B' - Right-sided signal.
The Laplace transform is a mathematical tool used to analyze signals and systems in the frequency domain. It is particularly useful in solving differential equations and studying the behavior of linear time-invariant (LTI) systems.
The Laplace transform of a signal x(t) is defined as X(s) = ∫[0 to ∞] x(t)e^(-st) dt, where s is a complex variable.
In the Laplace domain, the complex variable s can have different values. The poles of the Laplace transform are the values of s for which the transform becomes infinite. Poles provide important information about the behavior and characteristics of the signal.
Given Information
In this question, we are given that the Laplace transform of the signal x(t) has only one pole at s = 4. This means that the transform X(s) has a term of the form 1/(s - 4).
Explanation
To determine the nature of the signal x(t), we need to analyze the pole at s = 4.
When a pole is located in the left-half of the complex plane (i.e., Re(s) < 0),="" the="" corresponding="" signal="" x(t)="" is="" left-sided.="" this="" means="" that="" the="" signal="" is="" non-zero="" only="" for="" t="" />< />
When a pole is located in the right-half of the complex plane (i.e., Re(s) > 0), the corresponding signal x(t) is right-sided. This means that the signal is non-zero only for t > 0.
In this case, the pole is located at s = 4, which has a positive real part. Therefore, the signal x(t) is right-sided.
Conclusion
Based on the given information, we can conclude that the signal x(t) is a right-sided signal. Therefore, the correct answer is option 'B' - Right-sided signal.
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An absolutely integrable signal x(t) is known to have Laplace transform with only one pole at s = 4 the x(t) isa)Left sided signalb)Right sided signalc)Signal of finite durationd)Double sided signalCorrect answer is option 'A'. Can you explain this answer?
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