calculate.glla {doremi}

Calculation of derivatives using the GLLA method

Description

calculate.glla estimates the derivatives of a variable using the Generalized Local Linear Approximation (GLLA) method described in doi: 10.4324/9780203864746Boker et al.(2010). This method estimates the derivatives over a number of measurement points called the embedding number assuming an equally spaced time series.

Usage

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

Arguments

signal

is the input vector containing the data from which the derivatives are 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 embedding dimension, that is the number of points to consider for derivative calculation. Embedding must be at least #' 2 for the calculation of the first derivative (first order models) and at least 3 for the calculation of the second derivative (second order models).

n

is the maximum order of the derivative to calculate

Value

Returns a list containing three columns:

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

#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.glla(signal = signal, time = time, embedding = 5)