Some Intrinsic Properties of Tadmor–Tanner Functions: Related Problems and Possible Applications

Abstract

In this paper, we study some properties of an exponentially optimal filter proposed by Tadmor and Tanner. More precisely, we consider the problem for approximating the function of rectangular type F(t) by the class of exponential functions σadapt(t) about the Hausdorff metric. We prove upper and lower estimates for “saturation”—d (in the case q=2). New activation and “semi-activation” functions based on σadapt(t) are defined. Some related problems are discussed. We also consider modified families of functions with “polynomial variable transfer”. Numerical examples, illustrating our results using CAS MATHEMATICA are given.

Keywords

• exponentially optimal adaptive filter
• Hausdorff distance
• upper and lower bounds
• activation function
• modified families of functions with “polynomial variable transfer”