Analog Low Pass Prototype to a Digital Filter
This is a method to tranform an analog low pass with an angular frequency of 1 rad/s, called an analog low pass protype, into a desired digital lowpass, high pass, band pass, band stop and notch filter with specified frequency. The technique of this method is based on the frequency transformation in s-domain and bilinear z-transformation with pre-warping frequency as shown in table II below.
Form table II, to transform a transfer function H(s) of an analog low pass prototype into a digital filter just replaces s by H(z). In general way with the helpful of the Pascal's triangle, the relationships between the coefficients of the analog low pass prototype and the desired digital filter can be described as a matrix equation, called "Analog low pass prototype to digital filter Pascal matrix equation" as shown below:
This equation is a general formula to transform the coefficients of an analog low pass protoptype filter transfer function H(s) to the coefficients of a digital filter transfer function H(z) and it is described more detail in the sections below of transforming low pass to low pass, high pass, band pass,band stop, Notch digital filter.
Analog low pass prototype to digital low pass
Analog low pass prototype to digital high pass
Analog low pass prototype to digital band pass and band stop
Transforming an analog low pass protototype filter to a digital band stop filter is the same way as converting the low pass filter to a digital band pass filter. Only one different is the subscript of the coefficients in the matrix [Ai] and [Bi] are written in descending order.