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How is the continuous time impulse function defined in terms of the step function?
- a)u(t) = d(d(t))/dt
- b)u(t) = d(t)
- c)d(t) = du/dt
- d)d(t) = u2(t)
Correct answer is option 'C'. Can you explain this answer?
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How is the continuous time impulse function defined in terms of the st...
Using the definition of the Heaviside function, we can come to this conclusion.
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How is the continuous time impulse function defined in terms of the st...
The continuous-time impulse function, denoted as δ(t), is a fundamental concept in signal processing and systems theory. It is often used to represent an infinitesimally narrow pulse or spike in a continuous-time signal. The impulse function can be defined in terms of the step function, denoted as u(t), as follows:
Explanation:
The step function u(t) is defined as:
u(t) =
1, t >= 0
0, t < />
The derivative of the step function u(t) with respect to time, du/dt, can be calculated as:
du/dt =
0, t < />
∞, t = 0
0, t > 0
The derivative of the step function u(t) is zero for t < 0,="" remains="" undefined="" at="" t="0," and="" becomes="" infinite="" for="" t="" /> 0. This behavior is characteristic of the impulse function.
Now, let's consider the derivative of the impulse function δ(t), denoted as d(t). By definition, the impulse function δ(t) is the derivative of the step function u(t):
d(t) = du/dt
So, the correct answer is option 'C': d(t) = du/dt.
Explanation:
The step function u(t) is defined as:
u(t) =
1, t >= 0
0, t < />
The derivative of the step function u(t) with respect to time, du/dt, can be calculated as:
du/dt =
0, t < />
∞, t = 0
0, t > 0
The derivative of the step function u(t) is zero for t < 0,="" remains="" undefined="" at="" t="0," and="" becomes="" infinite="" for="" t="" /> 0. This behavior is characteristic of the impulse function.
Now, let's consider the derivative of the impulse function δ(t), denoted as d(t). By definition, the impulse function δ(t) is the derivative of the step function u(t):
d(t) = du/dt
So, the correct answer is option 'C': d(t) = du/dt.
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How is the continuous time impulse function defined in terms of the step function?a)u(t) = d(d(t))/dtb)u(t) = d(t)c)d(t) = du/dtd)d(t) = u2(t)Correct answer is option 'C'. Can you explain this answer?
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