A program was written to determine the low pass filter coefficients.
(Click here to view the code for the testing program)
The output of the program is as follows:
Results:
4 sample/cycle:
First order 3DB ratio = 0.7509617805480957
First order 6DB ratio = 0.5857863426208496
Second order 3DB ratio = 0.864356517791748
Second order 6DB ratio = 0.7667346000671387
8 sample/cycle:
First order 3DB ratio = 0.5857863426208496
First order 6DB ratio = 0.35640573501586914
Second order 3DB ratio = 0.6944746971130371
Second order 6DB ratio = 0.5298819541931152
16 sample/cycle:
First order 3DB ratio = 0.3318209648132324
First order 6DB ratio = 0.20199346542358398
Second order 3DB ratio = 0.4498744010925293
Second order 6DB ratio = 0.3215975761413574
32 sample/cycle:
First order 3DB ratio = 0.1793208122253418
First order 6DB ratio = 0.10701799392700195
Second order 3DB ratio = 0.26179075241088867
Second order 6DB ratio = 0.1777663230895996
64 sample/cycle:
First order 3DB ratio = 0.09365320205688477
First order 6DB ratio = 0.055086612701416016
Second order 3DB ratio = 0.14140748977661133
Second order 6DB ratio = 0.09343862533569336
128 sample/cycle:
First order 3DB ratio = 0.04792070388793945
First order 6DB ratio = 0.02794027328491211
Second order 3DB ratio = 0.0734248161315918
Second order 6DB ratio = 0.04789304733276367
256 sample/cycle:
First order 3DB ratio = 0.02424764633178711
First order 6DB ratio = 0.01407003402709961
Second order 3DB ratio = 0.037416934967041016
Second order 6DB ratio = 0.024243831634521484
4 sample/cycle:
First order 3DB ratio = 1.5537397589683533
8 sample/cycle:
First order 3DB ratio = 2.414218051433563
16 sample/cycle:
First order 3DB ratio = 5.02737563085556
32 sample/cycle:
First order 3DB ratio = 10.15314115381241
64 sample/cycle:
First order 3DB ratio = 20.355483129024506