Coefficient quantization effects on pole locations for state model digital filters

Second order digital filters realized through state equations are analyzed for the effects of quantization of the system matrix coefficients upon filter pole location. Sensitivity analysis techniques are used to develop expressions for the radial and angular components of the change in pole location for each system matrix for both absolute and normalized coefficient variations. Minimum pole sensitivity regions within the unit circle of the z-plane are shown for each system matrix. The system matrices are also compared regarding realizable pole grids, and overflow limit cycles.