Assertion (A.: It is observed that step function is first derivative o...
If response due to one standard signal is known then response due to other signals can also be derived.
Assertion (A.: It is observed that step function is first derivative o...
Understanding the Assertion and Reason
The assertion (A) states that a step function is the first derivative of a ramp function, and an impulse function is the first derivative of a step function. This statement is indeed true in the context of signal processing.
Key Points of Assertion (A):
- Ramp Function: A ramp function increases linearly over time. Its derivative represents the rate of change.
- Step Function: The step function is constant (zero) until a specific point, where it jumps to a value. The derivative of a ramp function is a step function, indicating an instantaneous change.
- Impulse Function: An impulse function is a theoretical function that represents an instantaneous spike in value. The derivative of a step function, which changes at a single point, is an impulse function.
Examining the Reason (R)
The reason (R) posits that the output time response follows the same sequence as that of the input functions based on the derived time response expression. This statement is also true but does not directly explain the assertion.
Key Points of Reason (R):
- Output Time Response: It is derived from the system's response to various input functions.
- Sequence of Functions: While the time response does follow the sequence of input functions, this does not clarify why the relationships between ramp, step, and impulse functions exist.
Conclusion
- Correctness of A and R: Both A and R are true statements. However, R does not explain A adequately.
- Option B: Thus, the correct answer is option 'B': Both A and R are true, but R is not the correct explanation of A.