Generate noise series with power law scaling exponent

Usage

noise_powerlaw(
  y = NULL,
  alpha = -1,
  N = 512,
  standardise = FALSE,
  randomPower = FALSE,
  seed = NA
)

y: Time series to use as a 'model'. If specified, N will be N = length(y), and the series will be constructed based on stats::fft(y).
alpha: The log-log spectral slope, the scaling exponent. Use 0 for white noise, negative numbers for anti-persistant noises: -1 for \(\frac{1}{f}\) noise, positive numbers for persistent noises, e.g. 1 for blue noise.
N: Length of the time series
standardise: Forces scaling of the output to the range [-1, 1], consequently the power law will not necessarily extend right down to 0Hz.
randomPower: If TRUE phases will be deterministic, uniformly distributed in [-pi,pi]. If FALSE, the spectrum will be stochastic with a Chi-square distribution. If y is not NULL this argument will be ignored.
seed: Provide an integer number to set the seed for the random number generator in order to get reproducible results. If NA (default) no user defined seed will be set,

Time series with a power law of alpha.

This R code was adapted from a Matlab script called powernoise.m by Max Little. The script contained the following commented text:

With no option strings specified, the power spectrum is