SavitzkyGolayMatrix

SavitzkyGolayMatrix[r,k]

gives a matrix corresponding to a smoothing kernel of radius r for performing polynomial regression of degree k.

SavitzkyGolayMatrix[{r1,r2},{k1,k2}]

gives a matrix for performing polynomial regression of degree k1 over a window of radius r1 along rows, and degree k2 over a window of radius r2 along columns.

SavitzkyGolayMatrix[r,k,n]

gives a matrix for performing the n^(th) derivative of a polynomial regression of degree k.

SavitzkyGolayMatrix[{r1,r2… },{k1,k2,…},…]

gives an array using the specified parameters for each direction i.

Details and Options

Examples

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Basic Examples  (3)

Compute a matrix kernel for quadratic interpolation over a window of radius 5:

Compute a smoothing kernel of length 11 using a cubic interpolation:

Plot the vector:

A Savitzky–Golay matrix to compute first derivatives in the horizontal dimension:

Scope  (3)

Create a 3D smoothing kernel:

A 3D derivative kernel:

A 3D derivative kernel along the first dimension:

Options  (1)

WorkingPrecision  (1)

By default, machine precision is used in internal computations:

Use exact precision:

Applications  (2)

Use a 2D SavitzkyGolayMatrix as a smoothing kernel in ImageConvolve:

Compute the horizontal derivative of an image:

Properties & Relations  (1)

The order of the polynomial does not extend beyond twice the window size:

Wolfram Research (2014), SavitzkyGolayMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html.

Text

Wolfram Research (2014), SavitzkyGolayMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html.

CMS

Wolfram Language. 2014. "SavitzkyGolayMatrix." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html.

APA

Wolfram Language. (2014). SavitzkyGolayMatrix. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html

BibTeX

@misc{reference.wolfram_2024_savitzkygolaymatrix, author="Wolfram Research", title="{SavitzkyGolayMatrix}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html}", note=[Accessed: 22-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_savitzkygolaymatrix, organization={Wolfram Research}, title={SavitzkyGolayMatrix}, year={2014}, url={https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html}, note=[Accessed: 22-December-2024 ]}