Analog to Digital Pascal Matrix Equation
Frequency transformation from s-domain to z-domain is a method to transform a transfer function H(s) of an analog filter in to a transfer function H(z) of a digital filter. There are two matrix equations which are used to design a digital filter, called, "Analog low pass prototype to digital Pascal matrix equation" and "Analog to digital Pascal matrix equation".
Transforming an analog low pass prototype to a digital low pass, high pass, band pass, band stop, narrow band filter.
Transforming an analog filters to an analog low pass prototype filter.
Transforming any type of analog filter to a digital low pass, high pass, band pass, band stop, narrow band filter.
Transforming an analog low pass prototype to a digital band pass.
Example
Transforming an analog band to a digital band pass.
The most common method to design a digital filter from a designed analog low pass prototype filter is by first transform a designed analog filter using frequency transformation in s-domain to the same class of the desired digital filter, and then applying the bilinear z-transformation with pre-warping as shown in a diagram below and form that, a matrix equation is derived, called, "Analog low pass prototype to digital filter Pascal matrix equation.
Another method to design a digital filter from an analog filter is introduced in the section "Analog to digital filter". The technique of this new method is done by transforming an analog low pass, high pass, band pass, band stop to an analog low pass prototype and then transforming that filter to a desired digital filter. as shown in the diagram below
***********************************************************************