Analog to Analog Filter

Analog to analog filter

Analog to analog Pascal matrix equation

Analog to analog Pascal matrix equation is used to convert an analog filter to another analog filter. This equation is derived from frequency transformation method which is to transform an analog low pass prototype to another analog filter such as low pass, high pass, band pass,band stop and narrow band filter. In this section will introduce the new method to design a desired analog filter from a given analog filter.

Transforming an analog low pass prototype filter to another analog filter :

Frequency transformation is a method to convert a low pass prototype which has the corner angular frequency at 1 rad/s to another types of analog filter as shown in the Table I. Where ωc is the corner angular frequency of the desired low pass (Lp) and high pass (Hp), ωU and ωL are the upper and lower angular frequency of the desired band pass (Bp) and band stop filter (Bs). The relationship between the coeficients of a given analog low pass protoype filter and the coeficients of a desired analog filter can be written as a matrix equation below:

Transforming an analog filter to another analog filter :

Transforming an analog filter to anothe analog filter is a new method to design an analog filter. The technique of this method is based on the frequency transformation, inverting matrix and the wonderful application of the Pasca's triangle and from them, a matrix equation can be found, called "Analog to analog Pascal matrix equation as shown below

Example

Transforming an analog low pass filter to N-Octave band filter.

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