doremi (version 1.0.0)

calculate.gold: Calculation of derivatives using the GOLD method

Description

calculate.gold estimates the derivatives of a variable using the Generalized Orthogonal Local Derivative (GOLD) method described in 10.1080/00273171.2010.498294Deboeck (2010). The code available on this paper was extracted and adapted for non constant time steps. This method allows calculating over a number of measurement points (called the embedding number) derivatives with uncorrelated errors.

Usage

calculate.gold(signal, time, embedding = 3, n = 2)

Arguments

signal

is a vector containing the data from which the derivative is estimated.

time

is a vector containing the time values corresponding to the signal. Arguments signal and time must have the same length.

embedding

is an integer indicating the number of points to consider for derivative calculation. Embedding must be greater than 1 because at least two points are needed for the calculation of the first derivative and at least 3 for the calculation of the second derivative.

n

is the maximum order of derivative to estimate.

Value

Returns a list containing the following elements:

dtime- contains the time values in which the derivative was calculated. That is, the moving average of the input time over embedding points.

dsignal- is a data.frame containing n+1 columns and the same number of rows as the signal. The column k is the k-1 order derivative of the signal over embedding points.

embedding- number of points used for the derivative calculation.

n - the maximum derivative order calculated n

Examples

# NOT RUN {
#In the following example the derivatives for the function y(t) = t^2 are calculated.
#The expected results are:
#y'(t) = 2t and y''(t) = 2
time <- c(1:500)/100
signal <- time^2
result <- calculate.gold(signal = signal, time = time, embedding = 5)

# }