How to get transfer H(s) function out of impulse response

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noel_t

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The impulse response h(t) for a particular LTI system is shown below.

h(t) = [3e-3t + 5 e-2t + e-t (4 cos(3t)+ 6 sin(3t)) + e-4t] . u(t)

a) Plot the impulse response for h(t.)
b) Determine the transfer function H(s). Determine the locations of the poles and zeros of H(s) and plot them in the s-plane (‘x’ for poles, ‘o’ for zeros).
c) Plot the magnitude spectrum and phase spectrum of the transfer function.
d) Finally compare your results obtained with the MATLAB simulation.


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I need your help to give me guideline on how i can get the transfer function out of the given impulse response.
 

H(s) = L{h(t)}, where L{} is the Laplace transform.
 
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    noel_t

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I am having problem with defining the h(t) into matlab to plot the sequence.This is the code i am using.

y=((3*exp^(-3*t))+(5*exp^(-2*t))+(exp^-t)((4*cos(3*t))+(6*sin(3*t))+(exp^(-4*t))));

I am trying my best to use enough parentheses to prevent conflict. but i get this error.
>> y=((3*exp^-3*t)+(5*exp^-2*t)+e^-t((4*cos3*t)+(6*sin3*t)+(exp^-4*t)))
??? Error using ==> exp
Not enough input arguments.

Do you have any idea on how to best define t in here?
 

Code: 
y=((3*exp^-3*t)+(5*exp^-2*t)+e^-t((4*cos3*t)+(6*sin3*t)+(exp^-4*t)))
If this is your Matlab expression, I don't doubt that you get errors. Learn first about the required Matlab syntax for exponential or sine function!
 

Yea every thing is correct. but still getting this error i also checked yours

??? Error using ==> exp
Not enough input arguments.

even for this i also get the same error.........
y=(3*exp^(-3*t)) or y=(3*exp^-3*t)
 

In the Matlab documents I know, the required syntax is Y = exp(X) rather than exp^X
 
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    noel_t

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>> y=((3*exp(-3*t))+(5*exp(-2*t))+(exp(-t)*((4*cos(3*t))+(6*sin(3*t))+(exp(-4*t)))))
??? Error using ==> mtimes
Inner matrix dimensions must agree.
 

Try this:

Code: 
t=[0:0.1:10];
y= 3*exp(-3*t) + 5*exp(-2*t) + exp(-t).*(4*cos(3*t) + 6*sin(3*t)) + exp(-4*t);
plot(t, y);

However I think You should read something about Matlab.
 
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    noel_t

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I already found the Laplace of the the impulse response to get the transfer function as H(s) = L{h(t)}, where L{} is the Laplace transform.

Now in order to get the magnitude response and phase response, should i first take inverse laplace to get H(t) or directly can found from the S domain?
 

noel_t said:
Now in order to get the magnitude response and phase response, should i first take inverse laplace to get H(t) or directly can found from the S domain?
Click to expand...
If ROC of H(s) contains jw axis You can apply the substitution s = jw to get H(jw).
 
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    noel_t

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