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Related Experiment Video

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

On cosine-modulated wavelet orthonormal bases.

R A Gopinath1, C S Burrus

  • 1Dept. of Electr. and Comput. Eng., Rice Univ., Houston, TX.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|January 1, 1995
PubMed
Summary

This study presents cosine-modulated wavelet tight frames (WTFs) where the scaling function determines wavelets, simplifying design for transform coding. It offers various design techniques, focusing on K-regularity and smoothness for applications like image coding.

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Area of Science:

  • Signal Processing
  • Applied Mathematics
  • Image Processing

Background:

  • Multiplicity M, K-regular, orthonormal wavelet bases are crucial for transform coding.
  • Previous constructions required designing both scaling functions and wavelets for specific applications.
  • Cosine-modulated wavelet tight frames (WTFs) offer a parameterized class with unique scaling function-wavelet relationships.

Purpose of the Study:

  • To describe and parameterize the cosine-modulated class of multiplicity M wavelet tight frames (WTFs).
  • To present and discuss various design techniques for K-regular cosine-modulated WTFs.
  • To explore wavelet smoothness criteria and optimal designs for signal representation.

Main Methods:

  • Parameterization of cosine-modulated multiplicity M wavelet tight frames (WTFs).
  • Development and analysis of design techniques for K-regular WTFs.
  • Definition and application of smoothness criteria based on total variation for filter banks and WTFs.

Main Results:

  • A parameterized class of cosine-modulated WTFs is presented, where the scaling function uniquely determines wavelets.
  • Several design techniques for K-regular cosine-modulated WTFs are described, with a focus on short filter lengths for coding applications.
  • Designs prioritizing wavelet smoothness using total variation are provided, alongside optimal designs for signal representation. All constructed WTFs are orthonormal bases.

Conclusions:

  • The cosine-modulated WTF framework simplifies wavelet design by linking scaling functions and wavelets.
  • Effective designs for K-regular and smooth WTFs are presented, suitable for transform coding and signal representation.
  • The study provides practical, orthonormal WTF constructions with analytical formulas in some cases.