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 ...