genIntegratedharmonic: genIntegratedharmonic function

In miscFuncs: Miscellaneous Useful Functions Including LaTeX Tables, Kalman Filtering, QQplots with Simulation-Based Confidence Intervals and Development Tools

genIntegratedharmonic function

Description

A function to generate basis vectors for integrated Fourier series.

Usage

genIntegratedharmonic(
  df,
  t1name,
  t2name,
  base,
  num,
  sname = "bcoef",
  cname = "acoef",
  power = FALSE
)

Arguments

df	a data frame containing a numeric time variable of interest
t1name	a character string, the name of the variable in df containing the start time of the intervals
t2name	a character string, the name of the variable in df containing the end time of the intervals
base	the fundamental period of the signal, e.g. if it repeats over 24 hours and time is measured in hours, then put 'base = 24'; if the period is 24 hours but time is measured in days, then use 'base = 1/7'
num	number of sin and cosine terms to compute
sname	character string, name for cosine terms in Fourier series (not integrated)
cname	character string, name for sine terms in Fourier series (not integrated)
power	legacy functionality, not used here

Details

If the non-integrated Fourier series is:

f(t) = sum_k a_k sin(2 pi k t / P) + b_k cos(2 pi k t / P)

then
int_t1^t2 f(s) ds = sum_k a_k (base/(2 pi k))*(cos(2 pi k t1 / P) - cos(2 pi k t2 / P)) +
b_k (base/(2 pi k))*(sin(2 pi k t2 / P)-sin(2 pi k t1 / P))
where P is the funcamental period, or 'base', as referred to in the function arguments

Value

a data frame containing the start and end time vectors, together with the sin and cosine terms

miscFuncs documentation built on Nov. 2, 2023, 5:21 p.m.