f4110dfe-5252-470a-bf3f-d96a54efef83 33 3 5 decimal

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

Smooth data set and extract Fourier polynomial

data_1 1 0.132 - 2 0.11 - 3 0.045 4 0.0045 5 0.138 - 6 0.467 7 0.5 8 0.78 9 1.342 10 0.993 11 1.105 12 1.119 13 1.18 14 1.143 15 0.655 16 1.008 17 0.771 18 1.208 19 0.938 20 0.783 21 0.734 22 0.763 23 1.044 24 0.754 25 0.797 252 mat :

data_2 26 1.086 27 0.426 28 0.563 29 0.814 30 0.665 31 0.561 - 32 0.429 - 33 0.187 34 0.153 - 35 0.422 - 36 0.127 - 37 0.018 - 38 0.247 - 39 0.422 - 40 0.738 - 41 0.711 - 42 0.863 - 43 0.769 - 44 0.485 - 45 0.79 - 46 0.737 - 47 0.708 - 48 0.965 - 49 0.899 - 50 0.947 - 252 mat :

data_3 51 0.871 - 52 1.138 - 53 1.191 - 54 0.046 - 55 1.016 - 56 1.275 - 57 0.617 - 58 0.908 - 59 1.09 - 60 0.972 - 61 0.594 - 62 0.5 - 63 0.346 - 64 0.191 - 65 0.177 - 66 0.362 - 67 0.547 - 68 0.455 69 0.417 70 0.129 - 71 0.352 72 0.906 73 0.386 74 0.047 - 75 0.214 252 mat :

data_4 76 0.309 77 0.615 78 0.846 79 0.698 80 0.819 81 1.113 82 1.042 83 1.114 84 0.653 85 0.667 86 0.657 87 0.846 88 0.547 89 0.053 90 1.244 91 1.046 92 0.793 93 0.383 94 0.335 95 0.272 96 0.537 97 0.248 98 0.67 99 0.226 - 100 0.208 252 mat :

XY data_1 data_2 data_3 data_4 stack :

X XY 1 col :

Y XY 2 col :

N XY rows : 100

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

ω 2 π N / * : 0.062832

Δx X N el X 1 el - (N 1 - / : 1

u λ u X 1 el - (ω Δx / * :

Δx 1

0.05 λ 0.05969 -

a b c spec . 12 black 13 mat :

n 0 N range A n 1 + el 2 N / Y k 1 + el n k * ω * cos * k 0 N 1 - sum * eval : B n 1 + el 2 N / Y k 1 + el n k * ω * sin * k 0 N 1 - sum * eval : 21 line for

pts XY a b c spec pts :

Experiment smoothing

Smoothing factor =>

sm 10 :

Y Mean 0.167055

u B39 A 1 el 2 / A n 1 + el u λ n * cos * B n 1 + el u λ n * sin * + (n 1 sm sum + 11 line :

A 1 el 2 / 0.167055

fit x 1100 1.125 range : i 1 x length range v i el x i el B39 eval : 11 line for x v augment 31 line :

Fourier Budapest "B39" polynomial adjustable smoothing

pts fit 2 1 sys

XY 1 0.25 203 0.25 - 4 0.5 - 5 0.25 - 607 0.25 8 0.5 9 0.25 10011 0.25 - 12 0.5 - 13 0.25 - 14015 0.25 16 0.5 17 0.25 18019 0.25 - 20 0.5 - 21 0.25 - 22023 0.25 232 mat :

X XY 1 col :

Y XY 2 col :

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

N XY rows : 23

ω 2 π N / * : 0.273182

Δx X N el X 1 el - (N 1 - / : 1

u λ u X 1 el - (ω Δx / * :

a b c spec . 12 black 13 mat :

Δx 1

0.05 λ 0.259523 -

pts XY a b c spec pts :

n 0 N range A n 1 + el 2 N / Y k 1 + el n k * ω * cos * k 0 N 1 - sum * eval : B n 1 + el 2 N / Y k 1 + el n k * ω * sin * k 0 N 1 - sum * eval : 21 line for

Experiment smoothing

Smoothing factor =>

sm 3 :

Fourier Budapest39 is scalar u B39 A 1 el 2 / A n 1 + el u λ n * cos * B n 1 + el u λ n * sin * + (n 1 sm sum + 11 line :

Y Mean 0.021739 -

A 1 el 2 / 0.021739 -

fit x 146 1.125 range : i 1 x length range v i el x i el B39 eval : 11 line for x v augment 31 line :

Fourier Budapest "B39" polynomial adjustable smoothing

XY fit pts 3 1 sys x B39