Frequency Transformation
With
Pascal Matrix Equations
**** NGUYEN SI PHUOC ****
This work considers the involvement of Pascal’s triangle in the frequency transformation and the bilinear z-transformation method for converting the transfer function H(s) in the s-domain to the transfer function H(z) in the z-domain, as well as the inverse from H(z) to H(s). Matrix equations are derived by Nguyen Si Phuoc, namely the Pascal matrix equations. These equations are used to find the relationship between the coefficients of the transfer functions in the s-domain and z-domain. Additionally, in this work will mathematically view inverse matrix in the inverse Pascal matrix equation. The inverse matrix is difficult to determine due to the larger size of the matrix. To overcome this problem, some specific matrices are introduced, which will make computing and hand-calculation easier. Both matrix equations are powerful tools for transforming an analogue low-pass filter to a digital filter, and vice versa, as well as for transforming a digital filter to another digital filter.
Frequency transformation with Pascal matrix equations is a method to transform between analogue filters or between digital filters (low pass, high pass, band pass and band stop filter). The technique of this method is based on frequency transformation, bilinear z-transform with pre-warping frequency and a wonderful application of the Pascal’s triangle which is made for easier computing when transform from a filter to another one. And also from this method, three Pascal matrix equations are derived, they are called Analog to analog filter Pascal matrix equation, Analog to digital filter matrix equation and Digital to digital filter Pascal matrix equation which are used to design analogue and digital filters.
Now a day in filter design, the low pass prototype filter is chosen to convert into other types of analog filter or digital filter such as low pass, high pass, band pass and band stop filter by using frequency transformation and bilinear z-transformation with pre-warping frequency techniques. With the supporting of the Pascal’s triangle and two techniques were mentioned, in this paper will introduce a new method to transform between a filter to another one in a general mathematical way which is described as Pascal matrix equations. There are three kinds of the Pascal matrix equation, Analog to analog Pascal matrix equation, Analog to digital matrix equation and Digital to digital matrix equation, and they are used to convert from any analog filter to another analog filter, from any analog filter to digital filter and from any digital filter to another digital filter respectively. To sum up, the main purpose of this new method will give a new way to design a digital filter from any kind of filter.
My latest research
My research in Communication and Informatics
HIGH EFFICIENCY POWER AMPLIFIER FOR MOBILE COMMUNICATION SYSTEM
FOLLOW ME