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We can also do inverse Laplace transform using partial fraction expansion, and MATLAB can help you with that. If you want to find the partial-fraction expansion of ( 3 2) 4 4 4 ( ) 2 2 2 + + + + = s s s s s Y s, the following MATLAB program gives you the coefficients in the expansion. You write the coefficients of the numerator and the.
Compute the inverse Laplace transform of
1/s^2
. By default, the inverse transform is in terms of t
.Default Independent Variable and Transformation Variable
Compute the inverse Laplace transform of
1/(s-a)^2
. By default, the independent and transformation variables are s
and t
, respectively.Specify the transformation variable as
x
. If you specify only one variable, that variable is the transformation variable. The independent variable is still s
.Specify both the independent and transformation variables as
a
and x
in the second and third arguments, respectively.Inverse Laplace Transforms Involving Dirac and Heaviside Functions
Compute the following inverse Laplace transforms that involve the Dirac and Heaviside functions:
Find the inverse Laplace transform of the matrix
M
. Specify the independent and transformation variables for each matrix entry by using matrices of the same size. When the arguments are nonscalars, ilaplace
acts on them element-wise.If
ilaplace
is called with both scalar and nonscalar arguments, then it expands the scalars to match the nonscalars by using scalar expansion. Nonscalar arguments must be the same size.If
ilaplace
cannot compute the inverse transform, then it returns an unevaluated call to ilaplace
.Return the original expression by using
laplace
.Compute the Inverse Laplace transform of symbolic functions. When the first argument contains symbolic functions, then the second argument must be a scalar.