Roundoff noise upper bounds for cascaded recursive digital filter structures

Two upper bounds on the variance of roundoff noise at the output of a cascade digital filterstructure are established. Some of these bounds are easier to compute than the exact roundoff-noise variance.Algorithms utilising these bounds for the generation of low-noise cascade realisation (by proper pairing ofpoles and zeros and ordering of the 2nd-and/or lst-order sections) are suggested. An exhaustive search toobtain such a realisation becomes economically feasible because of the reduced complexity of computations.Illustrative examples are given, showing the application of one of these algorithms.