Limit cycle oscillations in a cascade of first-and second-order digital sections

An upper bound for the amplitude of the limit cycles at the output of each section of all-pole digital filters consisting of a cascade of first- and second-order sections is obtained when the input of the filter is zero. A bound for the quantization error can be obtained by slightly modifying the obtained result. Also, the effect of the zeros of the transfer function, when they exist, on these bounds is considered.