In an effort bless the 3 MULT complex multiply, I characterized the DC offset introduced in the butterflies in the FFT. I found initially that it was larger than I thought reasonable (of order the LSB per multiply, I seem to remember). The culprit was that the twiddle factors were all being truncated (instead of rounded) as simulink converted the floating point coefficients into fixed-point numbers. I solved this by rounding manually. This bug is hard to detect in practice because it does not apply to the first 2 stages of an FFT (so you would see it in the DC bin at a maximum of 1 LSB * 1/4 FFT window), and generally by making the FFT slightly noisier between bins because of imperfect signal cancellation. I doubt this bug has affected anyone's data in a perceptible way so far, but with correlators on the way, we'd have noticed at some point.
After the fix, I ran a random amplitude * e^iwt quantized at 18 bits through the cmult
* twiddle_factor and calculated the integrated change in complex amplitude over 10,000
clocks:
Type of multiplier, behavior between mults & adds
3 MULT complex multiply, truncating: -7e-3 offset over 1e5 clocks = -7e-8
3 MULT complex multiply, round even: -5e-3 offset over 1e5 clocks = -5e-8
4 MULT complex multiply, truncating: -5e-3 offset over 1e5 clocks = -5e-8
4 MULT complex multiply, round even: -5e-3 offset over 1e5 clocks = -5e-8
Do not confuse the rounding behavior internal to the multiplier with rounding behavior on the final result: truncating the final result will introduce a DC bias of order the LSB. What these results show is that internal to the cmult, truncating vs. rounding before adding doesn't affect the final 18 bits out for a 4 MULT, and it does slightly for the 3 MULT. For 18 bits out, this DC bias is of order the 23/24th bit.
Anyway, just an FYI.
Aaron Parsons
aparsons@astron.berkeley.edu
(work) 510-642-5189