Digital Signal Processing Reference
In-Depth Information
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Critial Path 4th
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Figure 7.5
Pipelining using cut-set (a) Two candidate cut-sets in a DFG implementing a 5-coefficient
FIR filter. (b) One level of pipelining registers added using cut-set 2
more registers. It is also worth mentioning that in many designs convenience is preferred over
absolute optimality.
The pipeline design implements the following transfer function:
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7.2.6 Cut-set Retiming of a Direct-form FIR Filter
Cut-set retiming can be applied to a direct-form FIR filter to get a transposed direct-form (TDF)
version. The TDF is formed by first reversing the direction of addition, successively placing cut-set
lines on every delay edge. Each cut-set line cuts two edges of the DFG, one in the forward and the
other in the backward direction. Then retiming moves the registers from the forward edge to the
backward edge. This transforms the filter from DF to TDF. This form breaks the critical path by
placing a register before every addition operation. Figure 7.6 shows the process.
Example: Consider an example of fine-grain pipelining where the registers are added inside a
computational unit. Figure 7.7(a) shows a 4-bit ripple carry adder (RCA). We need to reduce the
critical path of the logic by half. This requires exactly dividing the combinational cloud into two
stages. Figure 7.7(a) shows a cut-set line that divides the critical path into equal-delay logic, where
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Figure 7.6
FIR filter in direct-form transformation to a TDF structure using cut-set retiming.
(a) A 4-coefficient FIR filter in DF. (b) Reversing the direction of additions in the DF and applying
cut-set retiming. (c) The retimed filter in TDF
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