Hardware Reference
In-Depth Information
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Data flow graph (fixed point num.)
Mapping on 4x4 cells
Fig. 3.57
Data fl ow graph and mapping of FFT butter fl y calculation
a
b
Stage 1
Stage 2
Stage 3
Stage 1
Stage 2
Stage 3
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Original data flow
Transformed data flow
Fig. 3.58
Transformation of eight-point FFT data fl ow graph
After subtraction and addition are applied, the calculation results are obtained and
stored in the local memory.
The FFT algorithm is modified to obtain identical flow graphs at each stage.
This makes it possible to reduce the number of configurations and avoid the port-
number constraint of the local memory. Figure
3.58
shows both the original flow
(a) and the modified flow (b) of 8-point FFT. A square in each stage shows the
twiddle factor, Wab = exp (−2p
ib
/
a
), where “
a
” is positioned higher and “
b
” is
lower in the rectangles.
Two butterfly calculations can be mapped and executed on the cell array.
Therefore, for efficient use of the local memory, one butterfly calculation is applied
to the data with even numbers, and the other butterfly is applied to those with odd
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