By Topic

A generalized sampling theory without band-limiting constraints

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)
Unser, M. ; Swiss Federal Inst. of Technol., Lausanne, Switzerland ; Zerubia, J.

We consider the problem of the reconstruction of a continuous-time function f(x)∈H from the samples of the responses of m linear shift-invariant systems sampled at 1/m the reconstruction rate. We extend Papoulis' generalized sampling theory in two important respects. First, our class of admissible input signals (typ. H=L2) is considerably larger than the subspace of band-limited functions. Second, we use a more general specification of the reconstruction subspace V(ψ), so that the output of the system can take the form of a band-limited function, a spline, or a wavelet expansion. Since we have enlarged the class of admissible input functions, we have to give up Shannon and Papoulis' principle of an exact reconstruction. Instead, we seek an approximation f∈V(ψ) that is consistent in the sense that it produces exactly the same measurements as the input of the system. This leads to a generalization of Papoulis' sampling theorem and a practical reconstruction algorithm that takes the form of a multivariate filter. In particular, we show that the corresponding system acts as a projector from H onto V(ψ). We then propose two complementary polyphase and modulation domain interpretations of our solution. The polyphase representation leads to a simple understanding of our reconstruction algorithm in terms of a perfect reconstruction filter bank. The modulation analysis, on the other hand, is useful in providing the connection with Papoulis' earlier results for the band-limited case. Finally, we illustrate the general applicability of our theory by presenting new examples of interlaced and derivative sampling using splines

Published in:

Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on  (Volume:45 ,  Issue: 8 )