JSEP Fellowship: Fractal Noise Processes

Abstract

Three fractal stochastic processes were developed and defined. Their statistical properties were derived, and examples were provided. Fractal shot noise (FSN), which is formed when a homogeneous Poisson process is passed through a filter with a power-law decaying impulse response function, was defined. For certain parameters, FSN converges to fractional Gaussian noise, while for others it is a Levy-stable random process. The fractal shot-noise- driven Poisson process (FSNDP), formed when FSN becomes the rate function for a second Poisson process, was considered next. The FSNDP is a point process which has a power spectral density inversely proportional to frequency raised to an arbitrary power (between zero and unity) for certain ranges of parameters. Also developed, were two fractal renewal processes with power spectral densities similar to that of the FSNDP: a standard renewal process with arbitrary power between zero and unity, and a finite-valued, alternating renewal process where the power extends to two. Several applications of these three processes were examined in detail.

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Document Details

Document Type
Technical Report
Publication Date
May 31, 1993
Accession Number
ADA268841

Entities

People

  • George W. Flynn
  • Malvin C. Teich
  • Steven B. Lowen

Organizations

  • Columbia University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Charged Particles
  • Classification
  • Electrical Engineering
  • Engineering
  • Frequency
  • Gaussian Noise
  • Noise
  • Probability
  • Probability Density Functions
  • Radiation
  • Random Variables
  • Security
  • Shot Noise
  • Standards
  • Stochastic Processes
  • Universities

Readers

  • Aerospace Propulsion Engineering.
  • Statistical inference.