Stochastic Resonance & Signal Dithering

Optimal noise enhances detection of sub-threshold signals in nonlinear systems — adding noise can increase SNR.

0.70
1.5
0.50
1.00
SNR (estimated)
—
Stochastic resonance: a weak periodic signal + optimal noise → maximum output SNR.

In a bistable double-well V(x) = −x²/2 + x⁴/4, Kramers rate r_K ∝ exp(−ΔV/σ²).

SNR peaks at σ* where noise-driven transitions synchronize with the signal period — a hallmark of SR.