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System Simulator >
Discrete Time Analysis >
Linear Electrical Discrete Time Simulation with Impulse Invariance >
Step 2: Extracting the Poles and Zeros

Step 2: Extracting the Poles and Zeros

Each of the evaluated frequency responses is then converted to a rational form (ratio of two polynomials) using the Jordan fraction expansion and the Pade approximation. By solving for the roots of the denominator of the rational function, we get the unconstrained set of poles. Among those poles, some are not stable. The algorithm will check that and discard them. The algorithm then uses the least square minimization scheme to solve for the residues from a set of linear equations; this is to compensate for the fact that some bad poles may have been discarded. The pole-residue representation is then obtained, along with coupling factors to account for electrical sub-designs with multiple inputs and/or outputs.

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