This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

FourierDST

 FourierDST[list] finds the Fourier discrete sine transform of a list of real numbers. FourierDSTfinds the Fourier discrete sine transform of type .
• Possible types of discrete sine transform for a list of length giving a result are:
•  1 DST-I 2 DST-II 3 DST-III 4 DST-IV
• The inverse discrete sine transforms for types 1, 2, 3, 4 are types 1, 3, 2, 4, respectively.
• The list given in FourierDST[list] can be nested to represent an array of data in any number of dimensions.
• The array of data must be rectangular.
• If the elements of list are exact numbers, FourierDST begins by applying N to them.
Find a discrete sine transform:
Find the inverse discrete sine transform:
Find a discrete sine transform of type 1 (DST-I):
Find the inverse discrete sine transform:
Find a discrete sine transform:
 Out[1]=
Find the inverse discrete sine transform:
 Out[2]=

Find a discrete sine transform of type 1 (DST-I):
 Out[1]=
Find the inverse discrete sine transform:
 Out[2]=
 Scope   (2)
Use machine arithmetic to compute the discrete sine transform:
Use 24-digit precision arithmetic:
Two-dimensional discrete sine transform:
Four-dimensional discrete sine transform:
The list may have complex values:
You can use , , , or for the types , , , and respectively.
 Applications   (2)
Get an expansion for an odd function as a sum of sines:
The function values on a uniformly spaced grid with n points on :
Compute the DST-I and renormalize:
The function has, in effect, been periodized with a particular odd symmetry:
Plot the expansion error where the points are defined:
Approximate the second derivative for a function with zero boundary conditions:
Solve the wave equation for a plucked string:
Plot the solution as a surface:
DST-I and DST-IV are their own inverses:
DST-II and DST-III are inverses of each other:
The DST is equivalent to matrix multiplication:
FourierDST always returns normalized results:
To get unnormalized results, you can multiply by the normalization:
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