Time/scale-adjusted dyadic wavelet packet bases

Stephen P. Del Marco

doi:10.1117/12.236031

22 March 1996 Time/scale-adjusted dyadic wavelet packet bases

Stephen P. Del Marco

Proceedings Volume 2762, Wavelet Applications III; (1996) https://doi.org/10.1117/12.236031
Event: Aerospace/Defense Sensing and Controls, 1996, Orlando, FL, United States

Abstract

This paper generalizes the dyadic wavelet packet bases (DWP), developed by Coifman and Wickerhauser, to time/scale-adjusted DWP bases. These generalized DWP bases provide more flexibility in matching the time-scale characteristics of the input signal. Development of these generalized bases is achieved by combining the previously defined time-invariant DWP bases of Pesquet, Krim, Carfantan, and Proakis with a generalized scale sampling. The generalized scale sampling extends the usual dyadic sampling by adding a real-valued offset parameter to the integer power of two in the scale parameter. This offset parameter value is taken between zero and one. By combining both scale and translation generalizations, signal components existing between consecutive dyadic scales, or consecutive time translations, may be captured. It is shown how these DWP coefficients may be generated from a two step process; first projecting the input signal onto an appropriate space. Then, performing the usual wavelet low and highpass filtering operations, followed by downsampling. The projection operation is shown to be equivalent to a filtering operation. An expression for the filter taps is derived, and basic properties are proven. A translation-invariant transform defined on these scale-adjusted wavelet packets, is developed. An application to transient detection is presented, by developing a transient detector based on this transform. ROC curves, generated by Monte- Carlo simulation, are presented demonstrating detector performance. Detector performance is shown to be independent of the signal translation. It is further shown how matching the basis functions to the time-scale-frequency characteristics of the transient can provide improved detection performance.

Citation Download Citation

Stephen P. Del Marco "Time/scale-adjusted dyadic wavelet packet bases", Proc. SPIE 2762, Wavelet Applications III, (22 March 1996); https://doi.org/10.1117/12.236031

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
10 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Wavelets

Sensors

Signal detection

Signal to noise ratio

Sensor performance

Interference (communication)

Signal processing

Show All Keywords

Keywords/Phrases

Search In:

Publication Years