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»
Mathematica
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Mathematics and Algorithms
>
Calculus
>
Integral Transforms
>
FourierCosTransform
>
BUILT-IN MATHEMATICA SYMBOL
Integral Transforms and Related Operations
Tutorials »
|
FourierSinTransform
FourierTransform
FourierDCT
FourierCosSeries
FourierCosCoefficient
InverseFourierCosTransform
Convolve
See Also »
|
Fourier Analysis
Integral Transforms
More About »
FourierCosTransform
FourierCosTransform
gives the symbolic Fourier cosine transform of
expr
.
FourierCosTransform
gives the multidimensional Fourier cosine transform of
expr
.
MORE INFORMATION
The Fourier cosine transform of a function
is by default defined to be
.
Other definitions are used in some scientific and technical fields.
Different choices of definitions can be specified using the option
FourierParameters
.
With the setting
the Fourier cosine transform computed by
FourierCosTransform
is
.
Assumptions
and other options to
Integrate
can also be given in
FourierCosTransform
.
EXAMPLES
CLOSE ALL
Basic Examples
(3)
In[1]:=
Out[1]=
In[1]:=
Out[1]=
In[1]:=
Out[1]=
Scope
(4)
Elementary functions:
Special functions:
Generalized functions:
Multivariate transform:
Options
(3)
Fourier cosine transform of
BesselJ
is a piecewise function:
The default setting for
FourierParameters
is
:
Use a nondefault setting for a different definition of transform:
To get the inverse, use the same
FourierParameters
setting:
Use
GenerateConditions
->
True
to get parameter conditions for when a result is valid:
Properties & Relations
(2)
FourierCosTransform
and
InverseFourierCosTransform
are mutual inverses:
Results from
FourierCosTransform
and
FourierTransform
agree for even functions:
Possible Issues
(1)
Fourier cosine transform may be given in terms of generalized functions such as
DiracDelta
:
Neat Examples
(1)
SEE ALSO
FourierSinTransform
FourierTransform
FourierDCT
FourierCosSeries
FourierCosCoefficient
InverseFourierCosTransform
Convolve
TUTORIALS
Integral Transforms and Related Operations
MORE ABOUT
Fourier Analysis
Integral Transforms
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