Discrete scale vectors and decomposition of time-frequency kernels

Selin Aviyente; William J. Williams

doi:10.1117/12.406487

13 November 2000 Discrete scale vectors and decomposition of time-frequency kernels

Selin Aviyente, William J. Williams

Proceedings Volume 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X; (2000) https://doi.org/10.1117/12.406487
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

Previous work has shown that time-frequency distributions (TFDs) belonging to Cohen's class can be represented as a sum of weighted spectrograms. This representation offers the means of reducing the computational complexity of TFDs. The windows in the spectrogram representation may either be the eigenfunctions obtained from an eigen decomposition of the kernel or any complete set of orthonormal basis functions. The efficiency of the computation can further be increased by using a set of scaled and shifted functions like wavelets. In this paper, the concept of scaling is considered in discrete-time domain. The scale operator in the frequency domain is formulated and the vectors which correspond to the solutions of this eigenvalue problem in discrete-time are derived. These new eigenvectors are very similar in structure to the eigenvectors obtained from eigensystem decomposition of reduced interference distribution (RID) kernels. The relationship between these two sets of window functions is illustrated and a new efficient way of decomposing time-frequency kernels is introduced. The results are compared to the previous decomposition methods. Finally, some possible applications of these discrete scale functions in obtaining new time-frequency distributions are discussed.

Citation Download Citation

Selin Aviyente and William J. Williams "Discrete scale vectors and decomposition of time-frequency kernels", Proc. SPIE 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X, (13 November 2000); https://doi.org/10.1117/12.406487

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

Time-frequency analysis

Wavelets

Fourier transforms

Computer science

Electrical engineering

Lead

Matrices

Show All Keywords

Keywords/Phrases

Search In:

Publication Years