smooth

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Apply a smoothing to the vector x.

Usage
smooth(x {, type=0 {, m=1 {, s=1}}})
x
data vector
m
smoothing length; 0 < m <= nrow(x)/2 (default=1)
type
selects the smoothing algorithm (default=0)
s
output step size; 0 < s <= nrow(x)/2 (default=1)
Description

The smoothing function is selected by the argument type. 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:

{\displaystyle xs[i]={\frac {x_{i}.w_{0}+\sum _{j=1}^{m}{(x_{i-j}+x_{i+j}).w_{j}}}{w_{0}+2.\sum _{j=1}^{m}{w_{j}}}}}
type smoothing algorithm xs[i] =
0 average (x[i-m]+x[i-m+1]+..+x[i]+..+x[i+m-1]+ x[i+m]) / (2*m+1)
0 average with reciprocal weights (x[i-m]/(m+1)x[i-m+1]/m+..+x[i]+..+x[i+m-1]/m+ x[i+m]/(m+1)) / (1 + 2*m+1)
Result
A vector r with nrow(x)/s elements. The value r[j] is set to the value xs[j*s] of the smoothed data vector.

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