GPoM (version 1.0)

drvSucc: drvSucc : Computes the successive derivatives of a time series

Description

Computes the successive derivatives from one single time series, using the Savitzky-Golay algorithm (1964).

Usage

drvSucc(tin = NULL, serie, nDeriv, weight = NULL, tstep = NULL,
  winL = 9)

Arguments

tin

Input date vector which length should correspond to the variables of the input data (same number of lines).

serie

A single time series provided as a single vector.

nDeriv

The number of derivatives to be computed from the input series. The resulting number of time series obtained as an output will thus be nVar = nDeriv + 1.

weight

Weighting function of input data series. By default uniform weight is applied. This weighting function can also be used to apply the analysis piecewise using zeros and ones.

tstep

Time sampling of the input series. Used only if time vector tin is not provided.

winL

Number (odd) of points of the local window used for computing the derivatives along the input time series (series). The Savitzky-Golay filter is used for this purpose [1,2].

Value

A list containing: $serie The original time serie $tin The time vector corresponding to the original time series $tstep The time step (assumed to be invariant) $tout The time vector of the output series ^seriesDeriv A matrix containing the original variable (as smoothed by the filtering process) and its nDeriv + 1 first derivatives (note that winL values of the original time series will be lost both (winL - 1)/2 at the begining and at the end of the time series due to boundary effect).

References

[1] Savitzky, A.; Golay, M.J.E., Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry 36 (8), 1627-1639, 1964. [2] Steinier J., Termonia Y., Deltour, J. Comments on smoothing and differentiation of data by simplified least square procedure. Analytical Chemistry 44 (11): 1906-1909, 1972.

See Also

gloMoId, gPoMo, poLabs

Examples

# NOT RUN {
#############
# Example 1 #
#############
tin <- seq(0, 5, by = 0.01)
data <- 2 * sin(5*tin)
dev.new()
par(mfrow = c(3, 1))
# numerical derivation
drv <- drvSucc(tin = tin, nDeriv = 2, serie = data, winL = 5)
#
# plot original and filtered series
plot(tin, data, type='l', col = 'black', xlab = 't', ylab = 'x(t)')
lines(drv$tout, drv$seriesDeriv[,1], lty = 3, lwd = 3, col = 'green')
#
# analytic 1st derivative
firstD <- 10 * cos(5 * tin)
# plot both
plot(tin, firstD, type = 'l', col = 'black', xlab = 't', ylab = 'dx/dt')
lines(drv$tout, drv$seriesDeriv[,2], lty = 3, lwd = 3, col = 'green')
#
# analytic 2nd derivative
scdD <- -50 * sin(5 * tin)
# plot both
plot(tin, scdD, type = 'l', col = 'black', xlab = 't', ylab = 'd2x/dt2')
lines(drv$tout, drv$seriesDeriv[,3], lty=3, lwd = 3, col = 'green')

#############
# Example 2 #
#############
# load data
data("Ross76")
tin <- Ross76[,1]
data <- Ross76[,2]

# Apply derivatives
drvOut <- drvSucc(tin, data, nDeriv=4)
dev.new()
par(mfrow = c(3, 1))
# original and smoothed variable:
plot(drvOut$tin, drvOut$serie,
     type='p', cex = 1, xlab = 'time', ylab = 'x(t)')
lines(drvOut$tout, drvOut$seriesDeriv[,1], type='p', col='red')
lines(drvOut$tout, drvOut$seriesDeriv[,1], type='l', col='red')
# 1st derivative:
plot(drvOut$tout, drvOut$seriesDeriv[,2],
     type='p', col='red', xlab = 'time', ylab = 'dx(t)/dt')
lines(drvOut$tout, drvOut$seriesDeriv[,2], type='l', col='red')
# 2nd derivative:
plot(drvOut$tout, drvOut$seriesDeriv[,3],
     type='p', col='red', xlab = 'time', ylab = 'd2x(t)/dt2')
lines(drvOut$tout, drvOut$seriesDeriv[,3], type='l', col='red')


# }