Transforms
When you apply a transform keyword to a function, PTC Mathcad expects the function to have the default independent variable shown in the table below under the Function column. If your function has a different independent variable, you must type a comma followed by the name of the variable. PTC Mathcad returns the transformed function whose default variable is listed under the Transformed Function column.
|
Keyword
|
Transform
|
Default Variables
|
|
|---|---|---|---|
|
Function
|
Transformed Function
|
||
|
fourier
|
Fourier transform
|
t
|
ω
|
|
invfourier
|
Inverse Fourier transform
|
ω
|
t
|
|
laplace
|
Laplace transform
|
t
|
s
|
|
invlaplace
|
Inverse Laplace transform
|
s
|
t
|
|
ztrans
|
z-transform
|
n
|
z
|
|
invztrans
|
Inverse z-transform
|
z
|
n
|
• Find the Laplace transform of a function:
Since the independent variable t is the default function variable for laplace, you do not need to specify the variable name. PTC Mathcad returns the transformed function with the default variable s, as shown in the Transformed Function column above.
If the function uses a different independent variable, such as x, you must specify the variable after laplace.
• If the function has more than one variable, type the independent variable for the function to the right of laplace:
• You can change the default variable for the transformed function:
• You cannot use the default variable for the transformed function as the independent variable for the original function:
• To return results that are not fully simplified, use the modifier raw after the transform keyword. For example, compare the following results of ztrans:
• To evaluate the Laplace transform of piecewise functions, such as the Dirac delta or Heaviside step functions, when additional parameters are present, specify the signs of the parameters using the keyword assume. For example:
