Discrete Functions... Signal Simulation... A Study Using Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg66731] Discrete Functions... Signal Simulation... A Study Using Mathematica*From*: "Mohamed Al-Dabbagh" <mohamed_al_dabbagh at hotmail.com>*Date*: Sat, 27 May 2006 21:04:07 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Abstract: An attempt was made to analytically describe some basic functions which are provided with the libraries of mathematical functions of programming languages. This study will rely on Mathematica in calculating all numerical results. This study provides global methods to calculate some discrete functions, which were previously calculated by using low-level language techniques to chop digits. Using these definitions we can simulate digital signals without the need for IF statements and conditions. A comparison were made between the formulas provided by this study and some functions provided by Mathematica such as FractionalPart function that converges very slowly or does NOT converge at all to correct results. The formulas derived herein were applied to complex numbers and some interesting results were obtained, such as the integer part of a complex number equals the Floor of its real part, and will be without imaginary part, i.e. the integer part of a complex number is a real number! For the complete study: http://dabbagh2.fortunecity.com/disc Mohamed Al-Dabbagh