AN2768 Freescale Semiconductor / Motorola, AN2768 Datasheet - Page 28

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

Summary
Where flt indicates a MATLAB® floating-point FFT result and fix indicates an RCF result. The multiplier of 128 is
needed because of the scale down by 2 operation at each stage of the butterfly operation. Figure 24 shows the
point-wise error magnitude for 128 points across the frequency scale for the white noise input.
The 128-point FFT implementation was also tested with a sine wave of 0.1 Hz normalized frequency. The input
range of the sine wave was set to (–16384,+16383). Figure 25 shows how the original sine wave and the error
performance are plotted. The absolute errors across the frequency scale for the sine wave input are on the same
magnitude as the white noise errors. The vertical scale must be multiplied by 128. The shape of the error curves
indicates that the low-frequency components contain larger errors than the higher-frequency components.
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This application note describes the implementation of a 128-point DIT FFT algorithm on the Freescale MRC6011
RCF device. Because of the limited number of registers, the first half of the 128 input data is independent of the
second half of the data, until stage 7. The 128-point FFT butterfly flow is divided into three parts. Between the
stages, data regrouping is performed to facilitate the butterfly operations of the next stage. Data regrouping is
performed on RCF via register content swaps. The operation effectively converts inter-cell butterflies into intra-cell
butterflies so that the parallel RC array is used more efficiently in the FFT computation. Results from different
input test vectors have shown the effectiveness of these economic approaches.
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Summary
Figure 24. Absolute Error Performance of the 128-Point FFT with White Noise Input
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Implementation of a 128-Point FFT on the MRC6011 Device, Rev. 0
Absolute Error of FFT 128 by RCF as Compared to Matlab
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Frequency Index
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