DSP

复数模实用算法：Alpha max plus beta min algorithm

2019-07-13 16:11发布

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https://en.wikipedia.org/wiki/Alpha_max_plus_beta_min_algorithm
 https://dspguru.com/dsp/tricks/magnitude-estimator/
 I + jQ 的模 sqrt(I^2 + Q^2)
可以用公式： Mag ~=Alpha * max(|I|, |Q|) + Beta * min(|I|, |Q|)近似
 很有意思，把求二次方根这样一个非线性运算线性化了，而且精度也很高： ===================================================================== Alpha * Max + Beta * Min Magnitude Estimator Name Alpha Beta Avg Err RMS Peak (linear) (dB) (dB) --------------------------------------------------------------------- Min RMS Err 0.947543636291 0.392485425092 0.000547 -32.6 -25.6 Min Peak Err 0.960433870103 0.397824734759 -0.013049 -31.4 -28.1 Min RMS w/ Avg=0 0.948059448969 0.392699081699 0.000003 -32.6 -25.7 1, Min RMS Err 1.000000000000 0.323260990000 -0.020865 -28.7 -23.8 1, Min Peak Err 1.000000000000 0.335982538000 -0.025609 -28.3 -25.1 1, 1/2 1.000000000000 0.500000000000 -0.086775 -20.7 -18.6 1, 1/4 1.000000000000 0.250000000000 0.006456 -27.6 -18.7 Frerking 1.000000000000 0.400000000000 -0.049482 -25.1 -22.3 1, 11/32 1.000000000000 0.343750000000 -0.028505 -28.0 -24.8 1, 3/8 1.000000000000 0.375000000000 -0.040159 -26.4 -23.4 15/16, 15/32 0.937500000000 0.468750000000 -0.018851 -29.2 -24.1 15/16, 1/2 0.937500000000 0.500000000000 -0.030505 -26.9 -24.1 31/32, 11/32 0.968750000000 0.343750000000 -0.000371 -31.6 -22.9 31/32, 3/8 0.968750000000 0.375000000000 -0.012024 -31.4 -26.1 61/64, 3/8 0.953125000000 0.375000000000 0.002043 -32.5 -24.3 61/64, 13/32 0.953125000000 0.406250000000 -0.009611 -31.8 -26.6 =====================================================================
有空的时候研究下是什么原理

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