1. Stochastic Resonance
Adding Noise to a signal can help in its detection.
Just the right amount of noise must be added (resonance)
SR in Nature
Periodic ice age prediction
Crayfish warnings of approaching bass - a periodic fin motion
Dogfish spit noise to better detection.
Neurons

2. Stochastic Resonance What Causes SR? Mathematical Definition
Non-Additive Noise
Nonlinearities
Mathematical Definition
There is none

3. Example: Miyamoto Resonance
Add noise to image and threshold. Vary noise.

4. Most Studied System
1/s
dx/dt x
ax-bx3 +
 sin(t)
(t)

5. Numerics (Mataim et al. 1998)

6. Numerics (Mataim et al. 1998)

7. Numerics (Mataim et al. 1998)

8. Comparison of NP Optimal Detector
Coherent NP Correlator vs. Stochastic Resonance
Assumptions
Compared NP on input and after SR nonlinearity
Detector COHERENT
Noise = White Gaussian
Galdi, Pierro, Pinto (Phys Review E, June 1998).

9. Comparison of NP Optimal Detectors
Coherent NP Correlator vs. Stochastic Resonance (4 dB)
Galdi, Pierro, Pinto (Phys Review E, June 1998).

10. Noncoherent Noncoherent SR sign detector
Galdi, Pierro, Pinto (Phys Review E, June 1998).

11. Noncoherent Results
Noncoherent correlator is about 3dB worse than coherent.
Noncoherent SR is better than noncoherent correlator for low SNR
Galdi, Pierro, Pinto (Phys Review E, June 1998).