Analog to digital filter

Analog to digital Pascal matrix equation

The transfer function H(z) of the digital filers (low pass, high pass, band pass, band stop and narrow band) can be obtained from the transfer function H(s) of a designed analog filter. To design a digital filter, first transform a designed analog filter to an analog filter which the same class of the digital filter using Analog to analog Pascal matrix equation and then apply bilinear z-transformation with pre-warping. A block diagram in the figure.1 below, illustrates converting an analog filter to a low pass, high pass, band pass, band stop and narrow band digital filter..

The block diagram in the fig.1, there are two methods to design a digital filter from an desired analog fliter, which are:

* Design a digital filter from an analog low pass prototype filter:

The relationship between the coefficients of an analog low pass prototype and the coefficients of a digital filter can be described as a matrix equation below:

* Design a digital filter from any analog filter types:

This is a method to transform any analog filter such as low pass, high pass, band pass and band stop filter to a desired digital filter. The relationship betwwen the coefficients of a given analog filter and a desired digital filter can be obtained in a matrix equation, called, Analog to Digital Pascal matrix equation as below:

Example 1

Converting an analog low pass prototype filter to a digital filter

Example 2

Converting an analog filter to a digital filter