f_slow = 4e-05 yr^-1 = 1/25000 yr <- lower frequencies (larger periods) than this have to be PRESERVED! passband_A <=> f/f_sampling < 0.005 stopband_A <=> > 0.05 passband_B <=> f/f_sampling < 0.05 stopband_B <=> > 0.15 ripple_A = 3.5e-05 , suppress_A = 1e-05 ripple_B = 1e-09 , suppress_B = 1e-09 ======================================================================== dt0 = 1 yr, f_sampling0 = 1 yr^-1 filter no. 1 = A decimation factor K1 = 10 f_slow = 4e-05 yr^-1 < passband_A * f_sampling0 = 0.005 yr^-1 Passband check passed OK. f_max0 = 0.05 yr^-1 = 1/20 yr dt1 = 10 yr f_sampling1 = 0.1 yr^-1 > f_slow + f_max0 = 0.05004 Aliasing check passed OK. ------------------------------------------------------------------------ dt1 = 10 yr, f_sampling1 = 0.1 yr^-1 filter no. 2 = A decimation factor K2 = 10 f_slow = 4e-05 yr^-1 < passband_A * f_sampling1 = 0.0005 yr^-1 Passband check passed OK. f_max1 = 0.005 yr^-1 = 1/200 yr dt2 = 100 yr f_sampling2 = 0.01 yr^-1 > f_slow + f_max1 = 0.00504 Aliasing check passed OK. ------------------------------------------------------------------------ dt2 = 100 yr, f_sampling2 = 0.01 yr^-1 filter no. 3 = B decimation factor K3 = 3 f_slow = 4e-05 yr^-1 < passband_B * f_sampling2 = 0.0005 yr^-1 Passband check passed OK. f_max2 = 0.0015 yr^-1 = 1/666.667 yr dt3 = 300 yr f_sampling3 = 0.00333333 yr^-1 > f_slow + f_max2 = 0.00154 Aliasing check passed OK. ------------------------------------------------------------------------ ======================================================================== final sampling timestep dt = 300 yr final passband <=> f < 0.0005 yr^-1 <=> P > 2000 yr total ripple in the passband = 7.0001e-05 final stopband <=> f > 0.0015 yr^-1 <=> P < 666.667 yr minimum suppression in the stopband = 1e-09