Frequency-Damping Resolution of the Unit Disc: A Wavelet Idea.

Abstract

In this paper we introduce the numerical Laplace transform, a local time frequency analysis method which applies to causal signals. The numerical Laplace transform resolves the identity, has good time-frequency resolution, and adapts resolution windows according to the time delay. The numerical Laplace transform is equivalent to a wavelet transform in the frequency domain. The discretized version of the numerical Laplace transform is invertible. The kernel vectors of the transform are frame vectors that are nearly tight over a fairly wide range of parameters. We demonstrate this with several numerical experiments. The numerical Laplace transform resolves a causal signal onto the s-plane. With a suitable mapping, the signal is resolved into the frequency damping unit disc.

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Document Details

Document Type
Technical Report
Publication Date
Jul 29, 1996
Accession Number
ADA311768

Entities

People

  • Louis L. Scharf
  • Neng-taann Ueng

Organizations

  • University of Colorado Boulder

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Analytic Functions
  • Coefficients
  • Colorado
  • Computers
  • Decomposition
  • Digital Signal Processing
  • Electrical Engineering
  • Engineering
  • Fourier Analysis
  • Frequency
  • Frequency Domain
  • Gray Scale
  • Hilbert Space
  • Military Research
  • Signal Processing
  • Time Domain
  • Wavelet Transforms

Fields of Study

  • Engineering

Readers

  • Calculus or Mathematical Analysis
  • Image Processing and Computer Vision.