VLSI Digital Signal Processing Systems: Design and Implementation

15.4    SUBEXPRESSION SHARING IN DIGITAL FILTERS

This section considers the implementation of FIR digital filters using common subexpressions. Both canonic signed digit (CSD) (see Section 13.6.1) and two’s complement fixed-point representations with 1 integer bit are used in this section. Quantization of FIR digital filters using a specified number of signed power-of-two (SPT) terms is described in Appendix G.

Example 15.4.1    This example considers an example of common subexpression elimination within a single multiplication

This may be implemented as

where >> i denotes an arithmetic shift-right-by-i-bit operation, and is same as the scaling operation Alternatively, this multiplication can be implemented as

which requires one less addition.

Fig. 15.1    General Transposed Direct-Form FIR Filter Structure.

As discussed in Section 15.3, subexpression elimination can be applied where ...