Exact constructions of square-root Helmholtz operator symbols: The focusing quadratic profile

2000 ◽  
Vol 41 (7) ◽  
pp. 4881-4938 ◽  
Author(s):  
Louis Fishman ◽  
Maarten V. de Hoop ◽  
Mattheus J. N. van Stralen
Keyword(s):  
Square Root ◽  
Helmholtz Operator ◽  
Operator Symbols

Uniform high-frequency approximations of the square root Helmholtz operator symbol

Wave Motion ◽  
1997 ◽  
Vol 26 (2) ◽  
pp. 127-161 ◽  
Author(s):  
Louis Fishman ◽  
A.K. Gautesen ◽  
Zhiming Sun
Keyword(s):  
High Frequency ◽  
Square Root ◽  
Helmholtz Operator ◽  
Operator Symbol

About the Complexity of Square Root Extraction Algorithms in Finite Fields and Residue Rings

Vestnik MEI ◽  
2018 ◽  
Vol 5 (5) ◽  
pp. 79-88
Author(s):  
Sergey B. Gashkov ◽  
◽  
Aleksandr B. Frolov ◽  
Elizaveta Р. Popova ◽  
◽  
...  
Keyword(s):  
Finite Fields ◽  
Square Root ◽  
Root Extraction

The digital function filters – algorithms and applications

2013 ◽  
Vol 61 (2) ◽  
pp. 371-377
Author(s):  
M. Siwczyński ◽  
A. Drwal ◽  
S. Żaba
Keyword(s):  
Digital Filters ◽  
Phase Shifters ◽  
Square Root ◽  
Real Power ◽  
The Real ◽  
Distributed Parameters ◽  
Digital Modeling ◽  
Analysis And Synthesis ◽  
Basic Functions ◽  
Recursive Formulas

Abstract The simple digital filters are not sufficient for digital modeling of systems with distributed parameters. It is necessary to apply more complex digital filters. In this work, a set of filters, called the digital function filters, is proposed. It consists of digital filters, which are obtained from causal and stable filters through some function transformation. In this paper, for several basic functions: exponential, logarithm, square root and the real power of input filter, the recursive algorithms of the digital function filters have been determined The digital function filters of exponential type can be obtained from direct recursive formulas. Whereas, the other function filters, such as the logarithm, the square root and the real power, require using the implicit recursive formulas. Some applications of the digital function filters for the analysis and synthesis of systems with lumped and distributed parameters (a long line, phase shifters, infinite ladder circuits) are given as well.

Sign in / Sign up

Export Citation Format

Share Document