Wavelet based simulation of electronic circuits
Wavelet based simulation of electronic circuits
Disciplines
Electrical Engineering, Electronics, Information Engineering (50%); Mathematics (50%)
Keywords
-
RF Radio Frequency circuit simulation,
Wavelet based approximation,
Integrated Circuit Design,
Rearrangement Operators
This project is devoted to the development of algorithms for simulation, design and integration of high-GHz wireless systems-on-chip modules. Due to the high center frequencies involved, the classical multistep methods for solving ordinary differential-algebraic equations (DAEs) are not feasible anymore due to extrodinary run times. The algorithmic aims are twofold: search for an appropriate wavelet bases to sparsely represent signals on the one hand and reformulating the ordinary DAEs as partial differential equations (PDEs) on the other. The PDEs and DAEs are related by their characteristics. Determining sparse representations of the signal waveforms is supported by the mathematical analysis of entropy-minimizing best-bases algorithms and by the analysis of the induced rearrangement operators on Triebel-Lizorkin spaces.
In this project novel algorithms for the simulation, design and integration of high-GHz wireless systems-on-chip modules were developed. Such chips are described by huge nonlinear systems of differential-algebraic equations. Due to the high center frequencies encountered in Radio Frequency (RF) circuits, the classical multistep methods for solving ordinary differential-algebraic equations (DAEs) are not feasible anymore due to extraordinary run-times. The algorithmic aims are twofold: search for appropriate wavelet bases to sparsely represent signals on the one hand and reformulating the ordinary DAEs as partial differential equations (PDEs) on the other. The PDEs and DAEs are related by their characteristic curves. Results were published, e.g., in IEEE Trans. Computer-Aided Design and SIAM J. on Scientific Computing.Determining sparse representations of the signal waveforms is supported by - based on the Mallat/postorder algorithm - the analysis of the induced rearrangement operators on classical function spaces such as the Triebel-Lizorkin spaces. In the course of the project we determined the operator norm generated by Mallat/postorder rearrangements of the Haar system by showing that they are extremal in the class of Triebel-Lizorkin function spaces. The proof is published by DI Dr. J. Penteker in Quarterly J. Math. (Oxford).
- Universität Linz - 49%
- FH Oberösterreich - 51%
- Paul F. X. Müller, Universität Linz , associated research partner
Research Output
- 107 Citations
- 37 Publications
-
2018
Title Factorization of the identity through operators with large diagonal DOI 10.1016/j.jfa.2018.02.010 Type Journal Article Author Laustsen N Journal Journal of Functional Analysis Pages 3169-3207 Link Publication -
2014
Title Adaptive multi-rate wavelet method for circuit simulation. Type Journal Article Author Bittner K -
2011
Title Adaptive Wavelet-Based Method for Simulation of Electronic Circuits DOI 10.1007/978-3-642-22453-9_34 Type Book Chapter Author Bittner K Publisher Springer Nature Pages 321-328 -
2012
Title Trigonometric splines for oscillator simulation. Type Conference Proceeding Abstract Author Bittner K Conference 22nd International Conference Radioelektronika. -
2014
Title Uniform Estimates for Averages of Order Statistics of Matrices DOI 10.48550/arxiv.1411.6879 Type Preprint Author Lechner R -
2014
Title Interpolatory Estimates, Riesz Transforms and Wavelet Projections DOI 10.48550/arxiv.1409.2143 Type Preprint Author Müller P -
2014
Title Postorder rearrangement operators DOI 10.48550/arxiv.1410.2712 Type Preprint Author Penteker J -
2014
Title Localization and projections on bi-parameter BMO DOI 10.48550/arxiv.1410.8786 Type Preprint Author Lechner R -
2014
Title On almost everywhere convergence of orthogonal spline projections with arbitrary knots DOI 10.1016/j.jat.2013.12.004 Type Journal Article Author Passenbrunner M Journal Journal of Approximation Theory Pages 77-89 Link Publication -
2014
Title Unconditionality of orthogonal spline systems in L p DOI 10.4064/sm222-1-5 Type Journal Article Author Passenbrunner M Journal Studia Mathematica Pages 51-86 Link Publication -
2014
Title Optimal frequency sweep method in multi-rate circuit simulation DOI 10.1108/compel-11-2012-0346 Type Journal Article Author Bittner K Journal COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engin Pages 1189-1197 Link Publication -
2014
Title Pointwise estimates for B-spline gram matrix inverses DOI 10.3103/s1068362314020034 Type Journal Article Author Passenbrunner M Journal Journal of Contemporary Mathematical Analysis Pages 78-90 Link Publication -
2014
Title Homotopy Method for Finding the Steady States of Oscillators DOI 10.1109/tcad.2014.2302637 Type Journal Article Author Brachtendorf H Journal IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems Pages 867-878 -
0
DOI 10.13164/re Type Journal Article Journal Radioengineering -
0
Title Lecture notes on singular integrals, projections, multipliers and rearrangements. Type Other Author Müller Pfx -
2012
Title Simulation of the steady state of oscillators in the time domain. Type Conference Proceeding Abstract Author Brachtendorf Hg Conference DATE 12, Proceedings of the Conference on Design, Automation and Test in Europe. -
2012
Title Simulation of the steady state of oscillators in the time domain DOI 10.1109/date.2012.6176702 Type Conference Proceeding Abstract Author Brachtendorf H Pages 1355-1360 -
2012
Title Wavelet Algorithm for Circuit Simulation DOI 10.1007/978-3-642-25100-9_1 Type Book Chapter Author Bittner K Publisher Springer Nature Pages 5-11 -
2016
Title Multi-Rate Coupled Circuit-Device Simulation DOI 10.1109/radioelek.2016.7477334 Type Conference Proceeding Abstract Author Bittner K Pages 42-47 -
2016
Title Estimating Averages of Order Statistics of Bivariate Functions DOI 10.1007/s10959-016-0702-8 Type Journal Article Author Lechner R Journal Journal of Theoretical Probability Pages 1445-1470 -
2016
Title Latency Exploitation in Wavelet-Based Multirate Circuit Simulation DOI 10.1007/978-3-319-30399-4_2 Type Book Chapter Author Bittner K Publisher Springer Nature Pages 13-20 -
2015
Title Fast Algorithms for Adaptive Free Knot Spline Approximation Using Nonuniform Biorthogonal Spline Wavelets DOI 10.1137/14095354x Type Journal Article Author Bittner K Journal SIAM Journal on Scientific Computing Link Publication -
2015
Title Uniform estimates for averages of order statistics of matrices DOI 10.1214/ecp.v20-3992 Type Journal Article Author Lechner R Journal Electronic Communications in Probability Link Publication -
2015
Title Estimating averages of order statistics of bivariate functions DOI 10.48550/arxiv.1507.06227 Type Preprint Author Lechner R -
2016
Title Trigonometric Splines for Oscillator Simulation DOI 10.48550/arxiv.1604.07607 Type Preprint Author Bittner K -
2016
Title Latency Exploitation in Wavelet-based Multirate Circuit Simulation DOI 10.48550/arxiv.1604.07668 Type Preprint Author Bittner K -
2016
Title Adaptive Multi-rate Wavelet Method for Circuit Simulation DOI 10.48550/arxiv.1604.07215 Type Preprint Author Bittner K -
2016
Title Fast Algorithms for Adaptive Free-Knot Spline Approximation Using Non-Uniform Biorthogonal Spline Wavelets DOI 10.48550/arxiv.1604.07228 Type Preprint Author Bittner K -
2015
Title Factorization of the identity through operators with large diagonal DOI 10.48550/arxiv.1509.03141 Type Preprint Author Laustsen N -
2015
Title Absolutely summing operators and atomic decomposition in bi-parameter Hardy spaces DOI 10.48550/arxiv.1512.04790 Type Preprint Author Müller P -
2015
Title POSTORDER REARRANGEMENT OPERATORS DOI 10.1093/qmath/hav031 Type Journal Article Author Penteker J Journal The Quarterly Journal of Mathematics Pages 1103-1126 Link Publication -
2015
Title LOCALIZATION AND PROJECTIONS ON BI-PARAMETER BMO DOI 10.1093/qmath/hav028 Type Journal Article Author Lechner R Journal The Quarterly Journal of Mathematics Pages 1069-1101 Link Publication -
2015
Title Initial transient response of oscillators with long settling time DOI 10.7873/date.2015.0008 Type Conference Proceeding Abstract Author Brachtendorf H Pages 1162-1167 -
2013
Title Grid Size Adapted Multistep Methods for High $Q$ Oscillators DOI 10.1109/tcad.2013.2269800 Type Journal Article Author Brachtendorf H Journal IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems Pages 1682-1693 -
2016
Title Absolutely summing operators and atomic decomposition in bi-parameter Hardy spaces DOI 10.1090/proc/13300 Type Journal Article Author Müller P Journal Proceedings of the American Mathematical Society Pages 1221-1230 Link Publication -
2016
Title Interpolatory estimates, Riesz transforms and wavelet projections DOI 10.4171/rmi/910 Type Journal Article Author Müller P Journal Revista Matemática Iberoamericana Pages 1137-1162 Link Publication -
2013
Title p-Summing Multiplication Operators, dyadic Hardy Spaces and atomic Decomposition DOI 10.48550/arxiv.1310.4312 Type Preprint Author Müller P