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

来源：互联网发布：百度网盘mac版本编辑：程序博客网时间：2024/06/14 01:04

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 EstimatorName                  Alpha           Beta       Avg Err   RMS   Peak                                                 (linear)  (dB)  (dB)---------------------------------------------------------------------Min RMS Err      0.947543636291 0.392485425092   0.000547 -32.6 -25.6Min Peak Err     0.960433870103 0.397824734759  -0.013049 -31.4 -28.1Min RMS w/ Avg=0 0.948059448969 0.392699081699   0.000003 -32.6 -25.71, Min RMS Err   1.000000000000 0.323260990000  -0.020865 -28.7 -23.81, Min Peak Err  1.000000000000 0.335982538000  -0.025609 -28.3 -25.11, 1/2           1.000000000000 0.500000000000  -0.086775 -20.7 -18.61, 1/4           1.000000000000 0.250000000000   0.006456 -27.6 -18.7Frerking         1.000000000000 0.400000000000  -0.049482 -25.1 -22.31, 11/32         1.000000000000 0.343750000000  -0.028505 -28.0 -24.81, 3/8           1.000000000000 0.375000000000  -0.040159 -26.4 -23.415/16, 15/32     0.937500000000 0.468750000000  -0.018851 -29.2 -24.115/16, 1/2       0.937500000000 0.500000000000  -0.030505 -26.9 -24.131/32, 11/32     0.968750000000 0.343750000000  -0.000371 -31.6 -22.931/32, 3/8       0.968750000000 0.375000000000  -0.012024 -31.4 -26.161/64, 3/8       0.953125000000 0.375000000000   0.002043 -32.5 -24.361/64, 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

0 0