# 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 derivative of a polynomial regression of degree k.

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

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

# 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 SavitzkyGolay 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_2022_savitzkygolaymatrix, author="Wolfram Research", title="{SavitzkyGolayMatrix}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html}", note=[Accessed: 29-May-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_savitzkygolaymatrix, organization={Wolfram Research}, title={SavitzkyGolayMatrix}, year={2014}, url={https://reference.wolfram.com/language/ref/SavitzkyGolayMatrix.html}, note=[Accessed: 29-May-2023 ]}