impulse(c2d(tf([1],[1 0 0]),1),10)​与impulse(c​2d(tf([1],​[1 0 0]),1))的输出结果不同, 在t=1时候前者为0.5而后者为1？为什么？

impulse(c2d(tf([1],[1 0 0]),1),10)与impulse(c2d(tf([1],[1 0 0]),1))的输出结果不同, 在t=1时候前者为0.5而后者为1？求各位大佬解答！

Answer 1

[Suraj Kumar]

Hi Qu Tianxiang,

From what I gather, you are trying to understand the reasoning behind the difference between the outputs of MATLAB commands “impulse(c2d(tf([1],[1 0 0]),1),10)” and “impulse(c2d(tf([1],[1 0 0]),1))” at t=1.

Let us understand the working of both the functions in detail:

• In “impulse(c2d(tf([1],[1 0 0]),1),10)”, the function is called with a time vector of 10 samples thus impulse is computed at these specific points.
• But in case of “impulse(c2d(tf([1],[1 0 0]),1))”, the function is called without a time vector, so MATLAB automatically determines the time vector based on system dynamics.
• So, when you specify 10 samples the time vector might not include a point at exactly t=1 so it might be interpolating between points, whereas MATLAB’s default time vector includes more points and might exactly capture the impulse response.

Refer to the output below for a better understanding:

For more details on the “impulse” function in MATLAB, you can refer to the documentation below:

• https://www.mathworks.com/help/control/ref/dynamicsystem.impulse.html

Hope this is helpful!