By Topic

On the Approximation of L_{2} Inner Products From Sampled Data

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)
Kirshner, H. ; Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa ; Porat, M.

Most signal processing applications are based on discrete-time signals although the origin of many sources of information is analog. In this paper, we consider the task of signal representation by a set of functions. Focusing on the representation coefficients of the original continuous-time signal, the question considered herein is to what extent the sampling process keeps algebraic relations, such as inner product, intact. By interpreting the sampling process as a bounded operator, a vector-like interpretation for this approximation problem has been derived, giving rise to an optimal discrete approximation scheme different from the Riemann-type sum often used. The objective of this optimal scheme is in the min-max sense and no bandlimitedness constraints are imposed. Tight upper bounds on this optimal and the Riemann-type sum approximation schemes are then derived. We further consider the case of a finite number of samples and formulate a closed-form solution for such a case. The results of this work provide a tool for finding the optimal scheme for approximating an L2 inner product, and to determine the maximum potential representation error induced by the sampling process. The maximum representation error can also be determined for the Riemann-type sum approximation scheme. Examples of practical applications are given and discussed

Published in:

Signal Processing, IEEE Transactions on  (Volume:55 ,  Issue: 5 )