Page 417 - DSP Integrated Circuits

402 Chapter 9 Synthesis of DSP Architectures

five. This will only reduce the implementation cost slightly since the number of
inputs is small.

9.5.3 Numerically Equivalent Implementations of WDFs
Wave digital filters can also be implemented efficiently in a numerically equiva-
lent form [31, 34 - 37]. Sensitivity properties as well as the more important
pseudo-passivity is retained since proper magnitude quantizations are done in
front of the delay elements. Pseudo-passivity is required in order to suppress para-
sitic oscillations. The word length for the coefficients in the numerically equivalent
algorithm can be made short by exploiting the low sensitivity of WDFs to quantize
the adaptor coefficients properly. However, the most important factor is selection
of a good filter structure.
Generally, algorithms with a high degree of parallelism are better suited to
this approach, because the coefficient word length will be lower. Word length is
proportional to the number of adaptors through which the different computa-
tional paths pass. Therefore, wave digital lattice filters with branches imple-
mented using Richards' structures are preferable. Such a filter is shown in
Figure 9.18. The coefficient word length will be determined by only two adaptor
coefficients.

EXAMPLE 9.7
Determine the elements in the numerically equivalent form for the lattice wave
digital filter shown in Figure 9.18. Scaling multipliers corresponding to transform-
ers in the reference filter have been inserted in order to scale the signal levels
using Z/2-norms. Assume the following coefficient values which have been opti-
mized for a conventional implementation using canonic signed digit code (see sec-
tion 11.4):