Theory and Application of the Wavelet Transform to Signal Processing

Abstract

Recently, a new representation of square summable functions has been found that displays some sense of locality in time. Its continuous version is called the wavelet transform, and discrete version is called the wavelet expansion. This report presents several theoretical and practical aspects of these new representations in the context of signal theory and a signal processing. On the theoretical level, some new results are proved regarding the properties of wavelets. The work of others has also been extended. Two practical applications of the wavelet expansion are also presented. The first is the equivalent to passband filtering of analog signals, and the second is the derivation of an iterative restoration algorithm used to estimate the impulse response of a linear system. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 31, 1991
Accession Number
ADA239533

Entities

People

  • David M. Drumheller

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Convolution Integrals
  • Distortion
  • Doppler Effect
  • Equations
  • Filtration
  • Fourier Analysis
  • Fourier Series
  • Frequency
  • Linear Systems
  • Signal Processing
  • Stationary Processes
  • Stochastic Processes
  • Time Domain
  • Two Dimensional
  • Wavelet Transforms

Fields of Study

  • Engineering

Readers

  • Calculus or Mathematical Analysis
  • Radar Systems Engineering.
  • Wave Propagation and Nonlinear Chaotic Dynamics.