Power-Law Spectral Density (1/f Noise)

Generate colored noise with arbitrary spectral exponent α and analyze its PSD

Parameters

α=0: white α=1: pink (1/f) α=2: brown

Spectral Analysis

Target α—
Fitted slope (log-log)—
Noise type—
σ (std dev)—

Theory

1/f noise appears throughout nature: heart rate variability, neural activity, music, finance, geophysics. Generated via spectral shaping in Fourier space:

S(f) ~ f^{−α}

Filter white noise: X̃(f) = G(f) · f^{−α/2} where G is Gaussian white noise. Inverse FFT gives the time series. α=1 is the boundary between stationary (α<1) and non-stationary processes.