G. Cichon1, A.V. Shakhomirov2
1,2 St.-Petersburg state university of aerospace instrumentation (St.-Petersburg, Russia)
1 gordon.cichon@guap.ru; 2 shakhomirov@guap.ru
This paper investigates a linear approximation for the absolute value of a complex number. This is relevant for adjusting gain for various kinds of signals that are received as complex numbers. For this purpose, the absolute value of the signal has to be computed. This is represented by the Euclidean distance of the vector from the origin. E.E. Wright (Problem Corner. The Mathematical Gazette. Vol. 69, No. 447 (Mar., 1985), pp. 48-50) has suggested a linear approximation for the value of the absolute value of a complex number, and gives a set of sub-optimal parameters without further justification. In this paper we give a justification of the algorithm and determine the optimal set of parameters.
As a next step, we will investigate the implementation properties of this algorithms on various processors. This algorithm is useful many environments: in resource restricted microcontrollers with 8-, 16-, 32-bit arithmetic, in modern DSPS, and in high performance applications with SIMD extensions.
Cichon G., Shakhomirov A.V. Fast approximation of the Euclidian distance. Radiotekhnika. 2025. V. 89. № 6. P. 5−13. DOI: https://doi.org/10.18127/j00338486-202506-01 (In Russian)
- Weisstein E.W. Vector Norm. From MathWorld – A Wolfram Web Resource. URL: https://mathworld.wolfram.com/Vector-Norm.html (data obrashhenija 16.05.2024).
- Wright E.E. Problem Corner. The Mathematical Gazette. Mar. 1985. V. 69, № 447. Р. 48-50. URL: http://www.jstor.org/stable/3616455 (data obrashhenija 13.05.2024)
- Stoer J., Bulirsch R. Introduction to numerical analysis. Springer, 2002. URL: https://www.bibsonomy.org/bib-tex/204636a15cb65b397dad2e5b87f483aed/noll (data obrashhenija 13.05.2024).