Annals of Biomedical Engineering

, Volume 16, Issue 5, pp 483–494 | Cite as

The fractal random telegraph signal: Signal analysis and applications

  • Larry S. Liebovitch
Article
Received:
Revised:

Abstract

A random telegraph signal is a time series whose value S(t) at time t is either one of only two possible values. Many processes including chemical reactions, cell membrane ion channels, and electronic noise generate such signals. Usually, Markov models have been used to model and analyze such data. Instead, we present a new fractal random telegraph signal that is statistically self-similar in time. We show how to analyze such signals and apply those techniques to study burst noise in a defective operational amplifier and ion currents recorded through individual ion channels in a cell membrane.

Keywords

Signal processing Fractal Ion channel Kinetics Noise 

Nomenclature

A

proportionality constant in the power lawk=At1−D

Ac

proportionality constant for entering the closed state

Ao

proportionality constant for entering the open state

c (subscript)

closed level of the two state (open-closed) signal

D

fractal dimension

Dc

fractal dimension associated with entering the closed state

Do

fractal dimension associated with entering the open state

f(t)

probability density of the durationst in a state

k

transition rate (probability per unit time) of exiting a state

keff

effective transition rate measured at time scaleteff

kc(eff)

effective transition rate for entering the closed state

ko(eff)

effective transition rate for entering the open state

o (subscript)

open level of the two state (open-closed) signal

P(t)

cumulative probability distribution of the durationst in a state

S(t)

signal level at timet

t

time

teff

effective time scale at which a measurement is done

X(t)

state at timet

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Copyright information

© Pergamon Press plc 1988

Authors and Affiliations

  • Larry S. Liebovitch
    • 1
  1. 1.Department of Ophthalmology College of Physicians & SurgeonsColumbia UniversityNew York

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