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FourierDCT

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

FourierDCT[list]

gives the Fourier discrete cosine transform (type II) of list.

FourierDCT[list, m]

gives the type-m transform, m one of 1..4 or "I".."IV".

Notes The four real orthonormal types are self/pair-inverse: I and IV invert themselves; II and III invert each other. Exact input is numericalised with N first; list may be a rectangular nested array (transformed per axis). Machine and arbitrary-precision (MPFR) input are both supported.

Examples (3)

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (3)

In[1]:= FourierDCT[{0, 0, 1, 0, 1}]
Out[1]= {0.894427, -0.425325, -0.0854102, -0.262866, 0.58541}

In[2]:= FourierDCT[{1, 0, 0, 1, 2}, 1]
Out[2]= {1.76777, -0.853553, 1.06066, 0.146447, 0.353553}

In[3]:= FourierDCT[{1, 2 I, 3, 4 I}]
Out[3]= {2.0 + 3.0*I, -0.112085 - 1.46508*I, -0.707107 + 0.707107*I, 1.57716 - 1.68925*I}

Implementation notes

Attributes: Protected.

References

See also: N, NDArray