AN2768 Freescale Semiconductor / Motorola, AN2768 Datasheet - Page 22

• Manufacturer Part Number: AN2768
• Description: Implementation of a 128-Point FFT on the MRC6011 Device
• Manufacturer: Freescale Semiconductor / Motorola

Fixed-Point and Precision Issues
The data exchange operation for this group of data is shown in Figure 19. After data regrouping, intermediate data
is transferred into the R4, R0, R5 and R1 registers, which are the same input registers for stage 1 butterflies. The
stage 2 butterfly can then reuse the code from stage 1.
4
For FFT on fixed-point processors such as the MRC6011 device, finite precision is limited by the number of bits
available in the number representation and by the effects of finite arithmetic operations (truncation and rounding).
It is important to understand that the magnitude of the complex FFT data changes through the various stages of
calculation. Figure 20 shows how two complex numbers at the input of the DIT butterfly combine to give two
outputs. First, Vector B is multiplied by the twiddle factor. Since all twiddle factors in the FFT have the form
which has unit magnitude, the magnitude of B
nothing more than a rotation of the vector B over the angle θ. The vectors B
to give the butterfly ouputs C and D, respectively.
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G1
G1
Fixed-Point and Precision Issues
Cell →
R8{0,*}
R9{0,*}
R4{0,*}
R0{0,*}
R4{0,*}
R0{0,*}
R5{0,*}
R1{0,*}
Figure 19. Group 1 Data Regroup After Stage 1 Butterfly Operation
MORPHO{
MORPHO{
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Implementation of a 128-Point FFT on the MRC6011 Device, Rev. 0
1
CELL{*,0} R4 = BYP{R8};
CELL{*,2} R4 = BYP{R8};
CELL{*,4} R4 = BYP{R8};
CELL{*,6} R4 = BYP{R8};
CELL{*,1} R1 = BYP{R0};
CELL{*,3} R1 = BYP{R0};
CELL{*,5} R1 = BYP{R0};
CELL{*,7} R1 = BYP{R0};
}
CELL{*,0} R0 = BYP{R9};
CELL{*,2} R0 = BYP{R9};
CELL{*,4} R0 = BYP{R9};
CELL{*,6} R0 = BYP{R9};
CELL{*,1} R0 = BYP{R0{*,$-1}};
CELL{*,3} R0 = BYP{R0{*,$-1}};
CELL{*,5} R0 = BYP{R0{*,$-1}};
CELL{*,7} R0 = BYP{R0{*,$-1}};
}
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2
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´
is the same as that of B. Multiplication by the twiddle factor is
3
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´
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and A are next added and subtracted
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Freescale Semiconductor
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8
e
–
jθ