J. Kauraniemi et al., DELTA-OPERATOR REALIZATIONS OF DIRECT-FORM IIR FILTERS, IEEE transactions on circuits and systems. 2, Analog and digital signal processing, 45(1), 1998, pp. 41-52
The use of the delta operator in the realizations of digital filters h
as recently gained interest due to its good finite-word-length perform
ance under fast sampling, We studied efficient direct form structures,
and show that only some of them can be used in delta configurations,
while others are evidently unstable, In this paper, we focus on the ro
undoff noise analysis, Of all the direct-form structures, the direct f
orm II transposed (DFIIt) delta structure has the lowest quantization
noise level at its output, This structure outperforms both the convent
ional direct-form (delay) structures, as well as the state-space struc
tures for narrow-band low-pass filters with respect to output roundoff
noise, Excellent roundoff noise performance is achieved at the cost o
f only a minor additional implementation complexity when compared with
the corresponding delay realization, Complexity of a signal processor
implementation of the DFIIt delta structure, which was found to be th
e most suitable delta structure for signal processors, is compared wit
h those of the direct form and state-space delay structures, In additi
on, some hardware implementation aspects are discussed, including the
minimization of the internal word length.