EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Exponential Splines


 CONTENTS
 Home Page
 News & Events
 People
 Publications
 Tutorials and Reviews
 Research
 Demos
 Download Algorithms

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

Cardinal Exponential Splines: Part II—Think Analog, Act Digital

M. Unser

IEEE Transactions on Signal Processing, vol. 53, no. 4, pp. 1439-1449, April 2005.



By interpreting the Green-function reproduction property of exponential splines in signal processing terms, we uncover a fundamental relation that connects the impulse responses of allpole analog filters to their discrete counterparts. The link is that the latter are the B-spline coefficients of the former (which happen to be exponential splines). Motivated by this observation, we introduce an extended family of cardinal splines—the generalized E-splines—to generalize the concept for all convolution operators with rational transfer functions. We construct the corresponding compactly-supported B-spline basis functions, which are characterized by their poles and zeros, thereby establishing an interesting connection with analog filter design techniques. We investigate the properties of these new B-splines and present the corresponding signal processing calculus, which allows us to perform continuous-time operations, such as convolution, differential operators, and modulation, by simple application of the discrete version of these operators in the B-spline domain. In particular, we show how the formalism can be used to obtain exact, discrete implementations of analog filters. Finally, we apply our results to the design of hybrid signal processing systems that rely on digital filtering to compensate for the nonideal characteristics of real-world analog-to-digital (A-to-D) and D-to-A conversion systems.

Please consult also the companion paper by M. Unser, T. Blu, "Cardinal Exponential Splines: Part I—Theory and Filtering Algorithms," IEEE Transactions on Signal Processing, vol. 53, no. 4, pp. 1425-1438, April 2005.


@ARTICLE(http://bigwww.epfl.ch/publications/unser0504.html,
AUTHOR="Unser, M.",
TITLE="Cardinal Exponential Splines: {P}art {II}---{T}hink Analog, Act
        Digital",
JOURNAL="{IEEE} Transactions on Signal Processing",
YEAR="2005",
volume="53",
number="4",
pages="1439--1449",
month="April",
note="")

© 2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.