# Signals and Systems | Impulse Response Problem

• haitham111
In summary, the conversation is about finding the impulse response for a system governed by the equation 3y(t)'+5y(t)=x(t)+x(t)'. The individual has attempted to find the homogeneous solution for h(t) in two different ways, but has not been successful. They have asked for help and someone suggests using Laplace. The individual then tries with Laplace and is able to obtain the correct answer.
haitham111

## Homework Statement

Find the impulse response for the systems governed by the following equations:
3y(t)'+5y(t)=x(t)+x(t)'[/B]

## The Attempt at a Solution

I tried to obtain the homogeneous solution for h(t)[/B]
and then I failed to obtain the coefficients of the solution

you need to show some more work for us to help you. Why don't you show us how you tried to obtain the solution

haitham111 said:

## Homework Statement

Find the impulse response for the systems governed by the following equations:
3y(t)'+5y(t)=x(t)+x(t)'[/B]

## The Attempt at a Solution

I tried to obtain the homogeneous solution for h(t)[/B]
and then I failed to obtain the coefficients of the solution
Change to Laplace.

rude man said:
Change to Laplace.
since the order of x(t) is the same order of y(t)
the general solution of h(t) is h(t)=Ay(t)homo u(t)+Bdelta(t)
and with sub. into the diff.eq i obtained A and B with coefficents equating method.

I tried with laplace, and it had the same answer of the first methodI think my problem is solved right now thank you all

## 1. What is an impulse response in signals and systems?

An impulse response is the output of a system when an impulse function, also known as a Dirac delta function, is applied as the input. It represents the system's characteristics and behavior, including its stability, linearity, and time-invariance.

## 2. How is the impulse response related to the frequency response?

The frequency response is the Fourier transform of the impulse response. This means that the frequency response can be obtained by taking the Fourier transform of the impulse response, and vice versa. The frequency response provides information about the system's behavior at different frequencies, while the impulse response describes the system's behavior in the time domain.

## 3. What is the significance of the impulse response in signal processing?

The impulse response is crucial in signal processing as it allows us to analyze and understand the behavior of a system. It also helps in designing and optimizing systems for specific applications. In addition, the impulse response is used in convolution, a fundamental operation in signal processing that combines two signals to produce a third signal.

## 4. Can the impulse response of a system change over time?

Yes, the impulse response of a system can change over time, but it depends on the system's properties. If the system is time-invariant, the impulse response will remain constant over time. However, if the system is time-varying, the impulse response will change as the system's properties change over time.

## 5. How can the impulse response be measured or estimated?

The impulse response can be measured or estimated using various techniques, such as applying an impulse input to the system and recording the output, or using mathematical models and simulations. Another common method is to use a known input signal, such as a sinusoid, and analyze the output to determine the system's impulse response. Additionally, specialized instruments and software can be used to measure the impulse response of a system accurately.

• Engineering and Comp Sci Homework Help
Replies
2
Views
1K
• Engineering and Comp Sci Homework Help
Replies
4
Views
1K
• Engineering and Comp Sci Homework Help
Replies
3
Views
5K
• Engineering and Comp Sci Homework Help
Replies
17
Views
5K
• Engineering and Comp Sci Homework Help
Replies
4
Views
1K
• Engineering and Comp Sci Homework Help
Replies
1
Views
2K
• Engineering and Comp Sci Homework Help
Replies
2
Views
4K
• Engineering and Comp Sci Homework Help
Replies
4
Views
1K
• Engineering and Comp Sci Homework Help
Replies
3
Views
1K
• Engineering and Comp Sci Homework Help
Replies
3
Views
2K