Change to Laplace.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]Homework Equations
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
since the order of x(t) is the same order of y(t)rude man said:Change to Laplace.
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.
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.
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.
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.
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.