A transfer function is a mathematical to describe the ratio between output and input of a system and it can be written in matrix form for an analog and a digital filter as shown in the equation (1),(2),(3) and (4) below. Let ‘A’ and ‘B’ are represented for the coefficient matrices in numerator and denominator of an analog filter, and similar for digital filter the letters ‘a’ and ‘b’ are used. The subscript ‘g’ denotes for ‘given’ and ‘d’ for ‘desired’.  

 

The transfer function of a given and desired analog filter: