Specify parameters for Fourier and inverse Fourier transforms

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Pref::fourierParameters(c, s)
Pref::fourierParameters([c, s])


Pref::fourierParameters(c, s), or the equivalent call Pref::fourierParameters([c, s]), specifies parameters used by the fourier and ifourier functions when computing Fourier and inverse Fourier transforms. See Example 1.

The Fourier transform of the expression f = f(t) with respect to the variable t at the point w is defined as follows:


The inverse Fourier transform of the expression F = F(w) with respect to the variable w at the point t is defined as follows:


c and s are the parameters of the Fourier transform controlled by Pref::fourierParameters.

By default, c = 1 and s = -1. Other common choices for the parameter c are or . Other common choices for the parameter s are 1, - 2 π, or 2 π.

Pref::fourierParameters() returns the current values of the Fourier parameters without changing them.

Pref::fourierParameters(NIL) restores the default settings c = 1, s = -1.

Pref::fourierParameters also controls the parameters used by the fourier::addpattern and ifourier::addpattern functions. See Example 2.

Environment Interactions

Changing Fourier parameters using Pref::fourierParameters can affect results returned by fourier and ifourier in the current MuPAD® session.


Example 1

Compute the Fourier transform of this expression using the default values c = 1, s = -1 of the Fourier parameters:

assume(Re(a) > 0):
fourier(t*exp(-a*t^2), t, w)

Use Pref::fourierParameters to change the values of the Fourier parameters to c = 1, s = 1. Then compute the Fourier transform of the same expression again:

Pref::fourierParameters(1, 1):
fourier(t*exp(-a*t^2), t, w)

Change the values of the Fourier parameters to and 1. Compute the Fourier transform using these values:

Pref::fourierParameters(1/(2*PI), 1):
fourier(t*exp(-a*t^2), t, w)

For further computations, restore the default values of the Fourier transform parameters:


Example 2

Use the default values of the Fourier transform parameters:


Add this new Fourier transform pattern for the function foo:

fourier::addpattern(foo(t), t, w, bar(w)):
fourier(foo(t), t, w)

The Fourier pair (foo, bar) is assumed to be valid for the current values of the Fourier parameters. When changing these parameters, you change the definition of the Fourier transform. Therefore, after changing Fourier parameters, the transform of foo(t) is not bar(w) anymore. The fourier function computes the result which is valid for the new parameters:

Pref::fourierParameters(c, s):
fourier(foo(t), t, w)

Now restore the Fourier transform parameters to their default values 1 and -1:


Return Values

List containing the previously set values of c and s