# Define a function - can anyone help me?

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#### Vauxdvihl

##### Member level 5 Define a function

Hi friends,

can somebody help to define the following function in the time domain (with A*exp(-_*_)+b*exp(-_*_)...........etc. ?

The function called:

1+s*0.5133154
f(s)=----------------------------------------------------
s^2*0.0010266308+s*0.30998924+4.4

Thank you very much for your help !!

Regards

#### Gemini1706

##### Member level 5 using matlab (if you do not want to do it by hand, out of laziness):

a=[0.5133154 1];
b=[0.0010266308 0.30998924 4.4];
[r,p,k]=residue(a,b)

yileds:
r=[523.8611 -23.8611]
p=[-287.0156 -14.9325]
k=[]

meaning that:
your transfer function could be expanded into partial fraction expansion as:
r(1)/(s-p(1)) + r(2)/(s-p(2)) + K
=523.8611/(s+287.0156 ) - 23.8611/(s+14.9325)

now, converting back to time domain:
=r(1)*exp(-j*p(1)) + r(2)*exp(-j*p(2))

you now the rest cheers...

#### Gemini1706

##### Member level 5 i meant: exp(-j*p(1)*t) ...etc (note the t I missed in the above work)

I guess you now. Hi,
Post such questions may be in Google groups or any such place or in beginners sections.