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VLSI Digital Signal Processing Systems: Design and Implementation by Keshab K. Parhi

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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

image

This may be implemented as

image

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

image

which requires one less addition. image

image

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

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

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