laplace of dirac delta function

my question is about the difference between this two definition of dirac delta function in Matlab:

dirac(t,1)

and

dirac(t-1)

I tried to apply the laplace transform and inverse laplace transform to this 2 functions and they gives me very different results:

   syms s t
  >> F_s=s+s^2; % definition of the function in s domain
  >> f_t=ilaplace(F_s)

f_t =

dirac(t, 1) + dirac(t, 2)

>> F_s=laplace(f_t)

F_s =

s^2 + s

>> F_s=laplace(dirac(t-1)+dirac(t-2))

% but if I use this definition for dirac delta function it gives a very diffrent answer...

F_s =

exp(-s) + exp(-2*s)

and my problem is that when i want to plot the function as:

t=1:0.1:4;
>> f_t1=dirac(t, 1) + dirac(t, 2);
Error using double.dirac
Too many input arguments.

It can't plot the function so I used the definition as :

dirac(t-1)+dirac(t-2)

but it gives a very different answer in Laplace transform... could you please explain the reason to me?

Thank you all

sahar

Answer 1

[Walter Roberson]

dirac(t,1) is the first derivative of dirac(), not dirac(t-1)