drvSucc {GPoM}

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 input time series.

serie

A single time series provided as a single vector.

nDeriv

The number of derivatives to be computed from the input time series. The resulting number of time series obtained in output will be nDeriv + 1.

weight

A vector providing the binary weighting function of the input data series (0 or 1). By default, all the values are set to 1.

tstep

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

winL

Number (exclusively odd number) of points of the local window used for computing the derivatives along the input time 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 containing the dates corresponding to the original time series

$tstep The time step (assumed to be regular)

$tout The time vector of the output series

seriesDeriv A matrix containing the original time series (smoothed by the filtering process) in the first column and its nDeriv + 1 successive derivatives in the next ones. Note that winL values of the original time series will be lost, that is (winL - 1)/2 at the begining and (winL - 1)/2 at the end of the time series due to a computation boundary effect).

Author(s)

Sylvain Mangiarotti, Mireille Huc

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, compDeriv

Examples

#############
# Example 1 #
#############
# Generate a time series:
tin <- seq(0, 5, by = 0.01)
data <- 2 * sin(5*tin)
dev.new()
oldpar <- par(no.readonly = TRUE)    
on.exit(par(oldpar))  
par(mfrow = c(3, 1))
# Compute its derivatives:
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]

# Compute the derivatives
drvOut <- drvSucc(tin, data, nDeriv=4)
dev.new()
oldpar <- par(no.readonly = TRUE)    
on.exit(par(oldpar))  
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')