genIntegratedharmonic: 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
)

Value

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

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