smooth

Apply smoothing to the vector or matrix x.

Usage

smooth(x {, type=0 {, m=1 {, s=1}}})

x

data vector or matrix

m

smoothing length; 0 < m ≤ nrow(x)/2 (default=1)

type

selects the weighting coefficients (default=0)

s

output step size; 0 < s ≤ nrow(x)/2 (default=1)

Description

The smoothed value xs[i] is computed from the data values x[i-m] to x[i+m]. The general form of the smoothing function is:

x s [ i ] = ∑ j = − m m x [ i + j ] . w [ j ] ∑ j = − m m w [ j ] {\displaystyle xs[i]={\frac {\sum _{j=-m}^{m}{x[i+j].w[j]}}{\sum _{j=-m}^{m}{w[j]}}}} $xs[i]={\frac {\sum _{j=-m}^{m}{x[i+j].w[j]}}{\sum _{j=-m}^{m}{w[j]}}}$

The weighting coefficients w[i] depend on the value of the argument type

type	w[j]
0	1	average
1	1 / (|j|+1)	distance weighted average

Result

A vector or matrix r with nrow(x)/s rows and the same number of clumns as x. The value r[j] is set to the value xs[j*s] of the smoothed data vector.

See also

optmm

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