A look at the smooth approximation to |f (x)| using some sigmoidal functions: Applications

In this article we give a brief overview of smooth approximation to |f (x)| using some sigmoidal func- tions. These studies can be successfully extended to perform sensitive analysis with other sigmoidal functions. More importantly, to show that the skillful combination of the two techniques ”smooth approximation” and ”polynomial variable transfer” can be used to modeling and simulating of filter characteristics and antenna patterns. Numerical examples are presented using CAS MATHEMATICA.