By Topic

On the use of singular value decomposition and decimation in discrete-time band-limited signal extrapolation

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Sullivan, B. ; Northwestern University, Evanston, IL ; Liu, B.

The problem of extrapolating a band-limited signal in discrete time is viewed as one of solving an underdetermined system of linear equations. Choosing the minimum norm least-squares (MNLS) solution is one criterion for singling out an extrapolation from all the possible solutions to the linear system. Use of the Moore-Penrose inverse yields the MNLS solution, and singular value decomposition (SVD) provides a means for implementing the Moore-Penrose inverse. An expression for the mean-square error incurred in solving a linear system via SVD is derived. This can be used to estimate the number of singular values needed to form the inverse. The error expression also indicates that decimation can be applied in the extrapolation problem to reduce the high computational cost of SVD without degrading the extrapolation. The results developed for the one-dimensional case are extended to higher dimensions. Examples of the SVD approach to extrapolation are given, along with examples using other extrapolation techniques for comparison. The SVD approach compares favorably with known MNLS extrapolation methods.

Published in:

Acoustics, Speech and Signal Processing, IEEE Transactions on  (Volume:32 ,  Issue: 6 )