A Comparative Study of the Frequency Responses of Some Existing Three-Dimensional Second Derivative Coefficient Sets with New Improvements PDF

Keywords

frequency noises, three-dimensional, second derivative

Abstract

The frequency responses of the all three-dimensional second derivative coefficient sets derived by Rao et al. (1970), along with that of their simple formula and the theoretical response of the second derivative operation, using an infinite number of points average approach, are presented. The frequency responses of the coefficient sets reveal: (a) the superiority of the coefficient sets derived following Peters' approach over those sets derived following Elkins' approach, (b) the superiority of the coefficient sets derived with a weightage of l/r^4 to all circles over those derived with a weightage of l/r^2 or without any weightage to all circles, (c) that many coefficient sets derived following Peters' approach give more accurate results than the simple formula, and also (d) the coefficient sets derived with preference to central point give better results than those derived with no preference to the central point. However, for the calculation of the second derivative, two new weight coefficient sets which use the least possible number of circles for obtaining average values and at the same time yield good results are developed by making use of Richardson's improvement formula of the derivative. We also present a comparative picture of the frequency responses of the derived sets, along with that of the best set of derived Rao et al.