Andrzej Kubaszek

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• Polynomial Numbers
• Repetitive Analysis
• Papers
• Contact
• PN algorithms library
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Polynomial Number Method

A polynomial pumber is generalised number. Digits of this number are elements of an arbitrary field, for example real numbers. The polynomial numbers in the transient analysis play similar role as complex numbers in AC analysis - these numbers allow to compute a solution of differential equations in the algebraic manner. A special field of utilisation of these numbers are systems described by non-rational transfer functions in Laplace or Z -transform domain (e.g. long lines).

Repetitive Analysis

Repetitive analysis of linear circuits is employed in optimisation, Monte-Carlo analysis, statistical analysis, parametric analysis, worst case analysis, real-time emulation, animation of characteristics etc. Repetitive analysis means fast calculations with multiple values for the circuit variables. This analysis is also used in calculations involving nonlinear circuits as most techniques for analysis of such circuits are iterative and require linearisation of a circuit at each iteration.

Discrete representations of generalized time domain function in symbolic-numerical analysis

Sequences of the samples, which correspond to abstract functions, like n-th derivative of Dirac's delta function, or function with negative delay operator can be used to filter characteristic of DSP algorithm closed in black box (SMACD 2006).

Polynomial Number algorithms library

• Interactive and editable notebooks ( observablehq.com)
• Polynomial_Numbers.ts (github.com), TypeScript / JavaScript, MIT
• Polynomial_Numbers.py (github.com), Python, MIT
• dash webapp (heroku.com)
• PNclass.zip, 31KB, 2007-002-12 - MATLAB class, LGPL
• SMACD_2006.ZIP, 489KB, 2006-010-07 - (Flash) Actionscript class pN.as inside, LGPL

Papers

• A. Kubaszek, L. Rozanski: The Polynomial Number Method for Computation Signal Waveforms in Frequency Dependent Parameter Inerconnection Lines, European Conference on Circuit Theory and Design (ECCTD), Kopenhaga 1991, pp. 709-718
  • AK-LR-ECCTD-91.pdf (50.1 KB)
  
  
• R. Dmytryszyn, A. Kubaszek: Sequence of Expressions Generation for the Repetitive Analysis Acceleration, 5-th International Workshop on Symbolic Methods and Applications in Circuit Design (SMACD-1998), Kaiserslautern, Germany 1998, pp. 154-159
  • RD-AK-SMACD98.pdf (120.6 KB)
  
  
• A. Kubaszek: A Fast Repetitive Transient Analysis of Large Circuits, 5-th International Workshop on Symbolic Methods and Applications in Circuit Design (SMACD), Kaiserslautern, Germany 1998, pp. 160-163
  • AK-SMACD98.pdf (68 KB)
  
  
• A. Kubaszek: Polynomial number method - computer implementation of some operational calculi, 6th International Conference on Methods and Models in Automation and Robotics (MMAR), Miedzyzdroje, Poland 2000, pp. 379-384.
  • AK-MMAR2000.pdf (81 KB)
  
  
• R. Dmytryszyn, A. Kubaszek: Multimethodical Approach and Generation of Sequence of Expressions for Acceleration of Repetitive Analysis of Analog Circuits, Analog Integrated Circuits and Signal Processing, An International Journal, Vol.31, Num. 2, Kluwer Academic Publishers, May 2002, pp. 147-159.
  • Full text version available at the Kluwer Academic Publishers on-line library.
     
• R. Dmytryszyn, A. Kubaszek, A. Wisz: Generation of Symbolic Determinant in Reverse Polish Notation , 7-th International Workshop on Symbolic Methods and Applications in Circuit Design (SMACD-2002), Sinaia, Romania 2002, pp. 53-56
   
• A. Kubaszek: Time Domain Repetitive Analysis of Analog Circuits with Transmission Lines , 8-th International Workshop on Symbolic Methods and Applications to Circuit Design (SMACD), Wroclaw, Poland 2004, pp. 67-70
  • AK-SMACD04.pdf (197 KB)
  
   
• A. Kubaszek: Discrete representations of generalized time domain function in symbolic-numerical analysis , 9-th International Workshop on Symbolic Methods and Applications to Circuit Design (SMACD), Firenze, Italy 2006.
  • AK-SMACD06.pdf (393 KB)
  
   

There are also some papers in polish >>

Contact

Post
 
Andrzej Kubaszek
Rzeszów University of Technology
al. Powstancow Warszawy 12,
35-959 Rzeszów
Poland

E-mail
kubaszek@prz.edu.pl

Web
https://pei.prz.edu.pl/~kubaszek/

Telephone
+4817 8651028

Feedback

Thank you for visiting. If you have any comments on this Web site, or would just like to get in touch, e-mail me at
kubaszek@prz.edu.pl