Steady-State Value of the Unit-Impulse Response

The steady-state value of the unit-impulse response can be determined by evaluating the transfer function at s = 0. In this case, the transfer function is given as 1/(s+1).

To find the steady-state value of the unit-impulse response, we substitute s = 0 into the transfer function:

H(0) = 1/(0+1) = 1/1 = 1

Therefore, the steady-state value of the unit-impulse response is 1.

Explanation:

1. Transfer Function:
The transfer function of a system describes its input-output relationship in the frequency domain. In this case, the transfer function is given as 1/(s+1), where s is the complex frequency variable.

2. Unit-Impulse Response:
The unit-impulse response of a system represents the system's output when an impulse function is applied as the input. It is a fundamental property used to analyze the behavior and characteristics of a system.

3. Steady-State Value:
The steady-state value of the unit-impulse response refers to the output value of the system after it has settled to a constant value. This occurs when the transient response of the system has decayed and only the steady-state response remains.

4. Evaluating the Transfer Function at s = 0:
To find the steady-state value of the unit-impulse response, we need to evaluate the transfer function at s = 0. Substituting s = 0 into the transfer function, we get:

H(0) = 1/(0+1) = 1/1 = 1

Therefore, the steady-state value of the unit-impulse response is 1.

Conclusion:
The steady-state value of the unit-impulse response for the given transfer function 1/(s+1) is 1. This means that the system settles to a constant output of 1 after the transient response has decayed.