What you have written makes no sense. I recognize that "x(dot)" is the derivative of x with respect to t but do you mean to have a "dot" next to the y in the next line? And what is "u"? Was that supposed to be y?khedira said:Hi,
given the state equations of a system,
x(dot) = Ax + Bu
y = Cx
is the impulse response function of this system C(e^(At))B? If not, how can i identify the impulse response from a given state equations? Please advise. Thank you.
HallsofIvy said:What you have written makes no sense. I recognize that "x(dot)" is the derivative of x with respect to t but do you mean to have a "dot" next to the y in the next line? And what is "u"? Was that supposed to be y?
That is, is the problem really
[tex]\frac{dx}{dt}= Ax+ By[/tex]
[tex]\frac{dy}{dt}= Cx[/tex]
?
An Impulse Response Function is a mathematical tool used in signal processing to measure how a system responds to a brief input, or "impulse". It is typically represented graphically as a curve or function that shows the output of the system over time in response to the impulse.
An Impulse Response Function can be measured by sending a short, high-energy pulse through the system and recording the output. This can be done using various techniques such as acoustic measurements, electrical measurements, or imaging techniques.
The Impulse Response Function is a useful tool for analyzing and understanding the behavior of a system. It can provide information about the system's characteristics, such as its frequency response, time delay, and distortion. It is also used in various applications, including audio and video processing, room acoustics, and image restoration.
An Impulse Response Function and a Frequency Response Function both provide information about a system's behavior. However, they measure different aspects of the system. The Impulse Response Function shows the system's response over time, while the Frequency Response Function shows the system's response at different frequencies.
An Impulse Response Function is commonly used in system identification, which is the process of determining a mathematical model that describes a system's behavior. By measuring the Impulse Response Function of a system, the parameters of the system's model can be estimated, allowing for prediction and control of the system's behavior.