FourierDCTMatrix
returns an n×n discrete cosine transform matrix of type 2.
FourierDCTMatrix[n,m]
returns an n×n discrete cosine transform matrix of type m.
Details and Options

- Each entry Frs of the discrete cosine transform matrix of type m is computed as:
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1. DCT-I 2. DCT-II 3. DCT-III 4. DCT-IV - The discrete cosine transform matrices of types 1, 2, 3, and 4 have inverses of type 1, 3, 2, and 4, respectively. »
- Rows of the FourierDCTMatrix are basis sequences of the discrete cosine transform.
- The result of FourierDCTMatrix[n].list is equivalent to FourierDCT[list] when list has length n. However, the computation of FourierDCT[list] is much faster and has less numerical error. »
- FourierDCTMatrix[…,WorkingPrecision->p] gives a matrix with entries of precision p.
Examples
open allclose allApplications (1)
Properties & Relations (2)
DCT matrix multiplied by a vector is equivalent to the discrete cosine transform of that vector:
FourierDCT is much faster than the matrix-based computation:
Discrete cosine transform matrix of type 1 is its own inverse:
Discrete cosine transform matrix of type 3 is an inverse of the type 2 matrix:
Discrete cosine transform matrix of type 4 is its own inverse:
Text
Wolfram Research (2012), FourierDCTMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/FourierDCTMatrix.html.
CMS
Wolfram Language. 2012. "FourierDCTMatrix." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FourierDCTMatrix.html.
APA
Wolfram Language. (2012). FourierDCTMatrix. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FourierDCTMatrix.html