Roundoff Noise Bounds Derived from Coefficient Sensitivities for Digital Filters
Date of Original Version
The sensitivities of the transfer function of a digital filter with respect to its coefficients are utilized to derive lower bounds on the roundoff noise output in the cases of L2 and L8 scaling for fixed-point arithmetic. General bounds are produced which apply to any filter structure if rounding is performed after multiplication and the filter has already been scaled. For the parallel and cascade forms, alternate bounds are derived which apply to rounding after multiplication or summation and which do not require prior scaling. The alternate bounds are thus independent (or nearly so) of pairing, ordering, and transposition. Examples are presented which show that the bounds are reasonably tight. © 1976, IEEE. All rights reserved.
IEEE Transactions on Circuits and Systems
Jackson, Leland B.. "Roundoff Noise Bounds Derived from Coefficient Sensitivities for Digital Filters." IEEE Transactions on Circuits and Systems 23, 8 (1976): 481-485. doi:10.1109/TCS.1976.1084247.