Savitzky-Golay Filter

## Usage

```
smooth_savitzky(x, y, ...)
# S4 method for numeric,numeric
smooth_savitzky(x, y, m = 3, p = 2)
# S4 method for ANY,missing
smooth_savitzky(x, m, p)
```

## Arguments

- x, y
A

`numeric`

vector. If`y`

is missing, an attempt is made to interpret`x`

in a suitable way (see`grDevices::xy.coords()`

).- ...
Currently not used.

- m
An odd

`integer`

giving the window size (i.e. the number of adjacent points to be used).- p
An

`integer`

giving the degree of the polynomial to be used.

## Value

Returns a `list`

with two components `x`

and `y`

.

## Details

This method is based on the least-squares fitting of polynomials to segments of \(m\) adjacent points.

## Note

There will be \((m - 1) / 2\) points both at the beginning and at the end of the data series for which a complete \(m\)-width window cannot be obtained. To prevent data loss, the original \((m - 1) / 2\) points at both ends of the data series are preserved.

## References

Gorry, P. A. (1990). General Least-Squares Smoothing and Differentiation by
the Convolution (Savitzky-Golay) Method. *Analytical Chemistry*, 62(6),
p. 570-573. doi:10.1021/ac00205a007
.

Savitzky, A. & Golay, M. J. E. (1964). Smoothing and Differentiation of
Data by Simplified Least Squares Procedures. *Analytical Chemistry*,
36(8), p. 1627-1639. doi:10.1021/ac60214a047
.

## See also

Other smoothing methods:
`smooth_loess()`

,
`smooth_rectangular()`

,
`smooth_triangular()`

,
`smooth_whittaker()`

## Examples

```
## Simulate data with some noise
x <- seq(-4, 4, length = 100)
y <- dnorm(x) + rnorm(100, mean = 0, sd = 0.01)
## Plot spectrum
plot(x, y, type = "l", xlab = "", ylab = "")
## Rectangular smoothing
unweighted <- smooth_rectangular(x, y, m = 3)
plot(unweighted, type = "l", xlab = "", ylab = "")
## Triangular smoothing
weighted <- smooth_triangular(x, y, m = 5)
plot(weighted, type = "l", xlab = "", ylab = "")
## Loess smoothing
loess <- smooth_loess(x, y, span = 0.75)
plot(loess, type = "l", xlab = "", ylab = "")
## Savitzky–Golay filter
savitzky <- smooth_savitzky(x, y, m = 21, p = 2)
plot(savitzky, type = "l", xlab = "", ylab = "")
## Whittaker smoothing
whittaker <- smooth_whittaker(x, y, lambda = 1600, d = 2)
plot(whittaker, type = "l", xlab = "", ylab = "")
```