How to get impulse response of an array of values aiming to apply fast fourier transform (fft) on impulse response array

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Basim Touqan 2016-11-6

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评论： Star Strider 2016-11-10

Dear colleagues, I have a challenge in building or extracting the transfer function in the form of Laplace based on a signal plotted in time domain in a pdf paper/articles. So far i managed to evaluate manually the coordinates of the signal in time domain by the following code in Matlab:

t0=[0 20 30 48 63 77 100 110 150 180 200 233 300 330 370 400 450 500 600 700 800];% points of t are obtained from the signal in whalley's paper% 
y0=[0 0.5 1 1.5 2 2.5 2.875 3 3.375 3.5 3.55 3.57 3.6 3.57 3.55 3.52 3.48 3.44 3.35 3.25 3.15];% points of y are obtained from the signal in whalley's paper% 
figure 
plot(t0,y0,'o');

The question is how can I get the impulse response of the signal y0(t0) and how can I get the frequency response of the same signal for the same time duration. At the end I want to get the frequency response to plot bode diagram and to try to conclude the transfer function in the Laplace transform from Bode plot. Any suggestion from you ends?

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Star Strider 2016-11-6

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You are doing ‘system identification’. MATLAB has an entire System Identification Toolbox devoted to it, and the Signal Processing Toolbox has the invfreqz function that will approximate it. This will be in discrete z-space. You can later use the bilinear transform to convert it to Laplace s-space. You will have to experiment to get the result you want.

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Basim Touqan 2016-11-10

编辑：Basim Touqan 2016-11-10

Mr. Strider, Now I got regarding the proper timing, the orginal time intervals were not equal, I have obtained now t0 points with similar intervals of 25 seconds so the sampling time is 25 seconds too. I think now every thing is fine. Thank you so much for valuable suuport