On the amplitude and time structure properties of 1fa noises

1
On the amplitude and time structure properties of
1/fa noises

• Z. Gingl, R. Mingesz and P. Makra
• Dept. of Experimental Physics
• University of Szeged, Hungary

2
About 1/f noises

• Very general occurrence
• Special properties
• Not completely understood
• New results, findings continuously
• Recent results on amplitude truncation special
  invariance of the power spectrum

3
Amplitude truncation of 1/fa noise
4
History of amplitude saturation investigations

• Diffusion noise generator driven by 1/f noise
  instead of 1/f2 noise output is close to 1/f
  (Trefan et al., 1989)
• Stochastic resonance in a Schmitt trigger driven
  by 1/f noise background noise remains 1/f
  (Kiss et al. 1992)
• PSD of 1/f noise is invariant to amplitude
  truncation under very general conditions (Gingl,
  Kiss, 1994)
• Extension to 1/fa noises (0ltalt2) (Gingl, Kiss,
  1996)
• Theoretical explanation (single level) (Ishioka
  et al.,2000)
• Extension to levels excluding mean, theory,
  numerical simulations (Gingl et al., Choi et al.,
  2001, now)
• Correlation properties of level-crossing
  intervals (now)

5
Invariance of PSD against truncationIf the mean
is between truncation levels
6
Very close levels at the mean
7
Positive part of the signal
8
Truncation by single level at the mean
theory o simulation
Invariance 0a1
9
General single level truncations

• Dependence of the exponent on the truncation
  level
• Strongest dependence a1 (1/f noise)

10
Relations between time structure properties and
amplitude truncation

• Spectrum of level crossing intervals 1/f?

0.30
0.25
0.20
0.15
g
0.10
0.05
0.00
0.0
0.5
1.0
1.5
2.0
a
11
Correlation between level crossings
t U,i
t L,i
t L,i1
12
Conclusions and open questions

• Partially confirmed by theory
• Unique features for ?1, possible reason for
  generality?
• Applications? (E.g. biomembrane channels?)
• Any role in natural processes?
• Prominently constructive role of ?1?(e.g. SR
  in FHN model, Nozaki et al., 1998-99, SR in flow
  of cars, L.Kish, S. Bezrukov,2000)
• Uniqueness in more aspects may help to understand
  processes