Computation of bounds for digital filter quantization errors

Spectral theory of operators is used to determine a general procedure for determining bounds on the difference between the states and outputs of a finite precision fixed-point digital filter and its infinite precision ideal counterpart. The results bound quantization errors for transients as well as limit cycles and apply when input signals are present. The procedure is extended to digital filters associated with difference equations, including the important special case of the basic second-order section.