Step response to an impulse response

In summary, the speaker is having trouble understanding how to find the step response of an LTIC system with a given impulse response. They have already sketched the impulse response, but are struggling to integrate it to find the step response. They mention that their text does not cover the step response and they would appreciate any help in figuring it out. However, they later state that they have figured it out on their own.
  • #1
EeCe
2
0
Hi all,

I'm having a lot of trouble understanding this step response:

Problem statement:

Consider an LTIC system with impulse response given by: h(t) = u(t) - u(t-2)

Sketch the step response s(t).

I've already sketched h(t)...but,
I know that the step response is found by integrating h(t) with respect to tau over the range -∞ to t. I know this is not hard, but for some reason I'm just having trouble figuring out what to do, and my text doesn't cover the step response at all (probably because it's so easy).

Any help if how to find the step response would be appreciated. Thanks
 
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  • #2
Well, I figured out on my own.
 

Related to Step response to an impulse response

What is the difference between step response and impulse response?

The step response of a system is the output when the input is a step function, which is a sudden change from one value to another. The impulse response, on the other hand, is the output when the input is an impulse, which is a short burst of energy at a specific time. In simple terms, the step response shows how a system reacts to a sudden change, while the impulse response shows how it reacts to a sudden burst of energy.

How are step response and impulse response related?

The step response and impulse response are mathematically related through the Fourier transform. The impulse response is the inverse Fourier transform of the transfer function, while the step response is the integral of the impulse response. In other words, the step response is the cumulative effect of all the impulses in the impulse response.

What does the shape of a step response tell us about a system?

The shape of a step response can tell us about the stability, damping, and time constants of a system. A fast rise time and small overshoot indicate a highly responsive and stable system. A slow rise time and large overshoot can indicate instability or underdamping. The time taken for the response to reach a steady state can also reveal information about the system's time constants.

How can we use step response and impulse response in control systems?

In control systems, step response and impulse response can be used to analyze the stability and performance of a system. By examining the shape of the response, we can determine if the system is stable and make adjustments to improve its performance. These responses can also be used to design controllers and predict the behavior of a system under different input signals.

What factors can affect the step response and impulse response of a system?

The step response and impulse response of a system can be affected by various factors such as the system's parameters, input signals, and external disturbances. The type of system (e.g., first-order, second-order) and its transfer function can also impact the shape of the responses. Additionally, the type and quality of the sensors and actuators used in the system can also influence the responses.

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