dcc27a26-cdc0-4549-a6f5-9aaa9b412260 21 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

data spec pts i 1 data rows range pt i el a b c spec : for Unest 'p' v pt 1 el : j 2 pt rows range v v pt j el stack : for data v augment 51 line :

Randomize a function

To regenerate new set of the randomized function, click-in the plot region => press F9. "level" = max level of random excursion...± level.

Random(n)=> Uniform ...  -1 < rnd < 1 n level rnd level n Random * level 2 / - 11 line :

x f span level populate randomize x 0 span 1 populate / range : i 1 x rows range y i el x i el f : for x y x rows level rnd + augment x y augment 21 mat 31 line :

level 0.5 :

XY 1 el noisy ≡ XY 2 el clean ≡ 21 mat

XY x sin 3 π * level 20 randomize : a b c spec . 8 black 13 mat : data XY 1 el a b c spec pts : 31 line

2 periods of noisy sine

data XY 2 el 2 1 sys

Collect for WINDOW data XY 1 el : X data 1 col : Y data 2 col : 31 line

over the 3π, @ population 20 randomize(f(x),n,level,populate) produces 20*3*π = 189 data pairs.

data rows 189

XY XY 1 el :

X XY 1 col :

Y XY 2 col :

Smath/User redefinition v n cfft v n al_fftc1d :

v n icfft v n al_fftc1dinv (:

r X Y Slope eval : 0.000624

m Y rows : 189

dd Y X r * - : D dd m cfft : w 4 : window size ≡ Low w 1 + : High w : 13 mat 41 line

Create the Fourier window j 1 m range j Low ≤ (m High - j ≤ (¤ DW j el D j el : 11 line 0 if for DW 21 line

dw mwabs dw mat2sys abs sys2mat ≡

dw DW m icfft eval X r * + :

vy dw mwabs :

Though, I don't understand the segmentation, I came to the conclusion it has to do with the natural vector length of both: al_fftc1d(v,n) ... al_fftc1dinv(v,n) in multiples of 32 pairs of data.

vy1 vy 16411 submatrix : vy2 vy 6512711 submatrix : vy3 vy 128 m 11 submatrix : vy vy1 vy2 - vy3 stack : 41 line

Two things in this WINDOW demo: 1. Fourier window can't recover the all range. 2. The noise level and distribution affects the end ranges, consequently the overall filter. Observe the Low => w+1 for equal end lengths. New plot: click-in the plot, press F9. Under the hood: tabulate 'DW'. Not so perfect but a damned effective filtering within a large profitable range.

Filter X vy augment :

data data a b c spec pts :

Observe end-bands. As it looks in this 
example, the profitable filter seems the 
inner range of the 'noisy XY'. I'm not 
aware of the "real life filtering". It 
could very well be  a piecewise technique.
More "Filters" in technical literature.
Observe  ... click-in the plot => F9. endband0 0.2 0 + 100 blue 15 mat : endband1 9.2 0 + 100 blue 15 mat : 21 line

XY 64 row XY 127 row 21 mat 3.15 0.08 - 12 mat 6.3 0.19 12 mat 21 mat

plot data Filter 3.15 1 3.15 1 - 22 mat 6.3 1 6.3 1 - 22 mat x sin endband0 endband1 91 sys :

plot

level 0.5