Symbolic Transforms

To evaluate the transform or inverse transform of a function, type the expression for the function to be transformed and either:

Then press [Enter].

If the function contains more than one variable, you must also type a comma and then type the independent variable for the function in the placeholder that appears to the right of the keyword.

Note: When you apply a transform keyword to a function, Mathcad expects the function to have the default independent variable shown in the table below, in the column under "Function." If your function has a different independent variable, you must type a comma, followed by the name of the variable.

Mathcad returns the transformed function whose default variable is listed in the column under "Transformed Function."

Keywords for Transforms:

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

Examples:

The following finds the Laplace transform of et:

Laplace transform of e to the t

Since the independent variable t is the default function variable for "laplace," you do not need to specify the variable name. Mathcad returns the transformed function with the default variable s, as shown in the column under "Transformed Function" in the table above.

However, if the function uses a different independent variable, such as x, you must specify the variable after "laplace."

Laplace transform of a function that doesn't use the default variable

If the function has more than one variable, you must also type the independent variable for the function to the right of "laplace":

Laplace transform of e to the -a times t.

To change the default variable for the transformed function, use the following syntax:

expr laplace, var1, var2

where var1 is the independent variable for the original function and var2 is the independent variable for the transformed function. For example,

Laplace transform specifying nondefault variables for both function and transform

Note that you cannot use the default variable for the transformed function as the independent variable for the original function. For example, the following returns an error:

e s laplace,s →

In this case, you must specify a variable for the transformed function that differs from the default variable, as shown in the preceding example.

Notes:

QuickSheet - Symbolic Transforms
QuickSheet - Fast Fourier Transforms

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