Symbolics > Working with Symbolics > Calculus > Transforms
  
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:
Click to copy this expression
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.
Click to copy this expression
• If the function has more than one variable, type the independent variable for the function to the right of laplace:
Click to copy this expression
• You can change the default variable for the transformed function:
Click to copy this expression
◦ You cannot use the default variable for the transformed function as the independent variable for the original function:
Click to copy this expression
In this case, you must specify a variable for the transformed function that differs from the default variable, as shown in the preceding example.
◦ If you use the default variable for the transformed function as the independent variable for the original function, PTC Mathcad returns the transformed function with the variable name doubled.
Click to copy this expression
You can specify a different variable for the transformed function using the syntax shown in the last example above.
• To return results that are not fully simplified, use the modifier raw after the transform keyword. For example, compare the following results of ztrans:
Click to copy this expression
• 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:
Click to copy this expression