Fractional Brownian motion synthesis (1/f^beta)

Generates a length-N fBm via spectral shaping of white noise with |f|^{-(H + 0.5)}, then cumulative integration. H = 0.5 recovers ordinary Brownian motion.

Usage

morie_dsp_fbm_synthesis(N, H = 0.5)

Arguments

N

Length.

H

Hurst exponent in (0, 1). Default 0.5.

Value

Numeric vector, length N.

References

Rangayyan & Krishnan (2015), Ch. 6, sec. 6.8; Mandelbrot & Van Ness (1968).

Examples

path <- morie_dsp_fbm_synthesis(N = 256L, H = 0.7)
length(path)
#> [1] 256