What is network synthesis and what are Hurwitz polynomials?

Network synthesis is the process of designing a network to realize a specified transfer function or impedance function. A Hurwitz polynomial has all roots in the left half of the s-plane, ensuring system stability. For a function to be realizable as a passive network, it must be a positive real function with non-negative real part for all Re(s) >= 0. Synthesis procedures like Cauer and Foster forms systematically extract L, C, R elements from driving-point impedances.