Inverse Laplace transform
ilaplace(
returns the Inverse Laplace Transform of
F
)F
. By default, the independent variable is
s
and the transformation variable is t
. If
F
does not contain s
,
ilaplace
uses the function
symvar
.
If any argument is an array, then ilaplace
acts
element-wise on all elements of the array.
If the first argument contains a symbolic function, then the second argument must be a scalar.
To compute the direct Laplace transform, use
laplace
.
For a signal f(t), computing the Laplace transform (laplace
)
and then the inverse Laplace transform (ilaplace
) of the
result may not return the original signal for t < 0. This is because the definition of laplace
uses the unilateral
transform. This definition assumes that the signal f(t) is only defined for all real numbers t ≥ 0. Therefore, the inverse result does not make sense for t < 0 and may not match the original signal for negative t. One way to correct the problem is to multiply the result of
ilaplace
by a Heaviside step function. For example, both
of these code blocks:
syms t;
laplace(sin(t))
and
syms t;
laplace(sin(t)*heaviside(t))
return 1/(s^2 + 1)
. However, the inverse Laplace
transform
syms s;
ilaplace(1/(s^2 + 1))
returns sin(t)
, not
sin(t)*heaviside(t)
.