Time-frequency localization in transforms, subbands, and wavelets: a critical review

Richard A. Haddad; Ali Naci Akansu; Adil Benyassine

doi:10.1117/12.138550

1 July 1993 Time-frequency localization in transforms, subbands, and wavelets: a critical review

Richard A. Haddad, Ali Naci Akansu, Adil Benyassine

Author Affiliations +

Optical Engineering, Vol. 32, Issue 7, (July 1993). https://doi.org/10.1117/12.138550

Abstract

In many still-image and video processing applications, the time-frequency localization properties of the decomposition technique are an important consideration. While bandwidth compression of the image requires operators with good localization in frequency, spatial features such as edge preservation demand a high degree of localization in time (or the spatial variable). These requirements compete with each other and one is secured at the expense of the other. The classical "uncertainty" principle in the continuous-time domain provides the back drop for this trade-off. Our purpose is to review recent extensions of this principle to the discrete-time case and to develop optimum wave forms. We review common features of block transforms, subband filter banks, and wavelets, and demonstrate how the discrete uncertainty can be used to evaluate these decomposition methods. In particular, we evaluate the trade-off between localization in time and in frequency for several proposed signal decomposition structures.

Citation Download Citation

Richard A. Haddad, Ali Naci Akansu, and Adil Benyassine "Time-frequency localization in transforms, subbands, and wavelets: a critical review," Optical Engineering 32(7), (1 July 1993). https://doi.org/10.1117/12.138550

Published: 1 July 1993

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