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b4df1e55-2034-48d7-bace-8401c4803aa1 31 15 12 decimal

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

Digitise a crappy trace from the web ...

... the signal under demo is very crappy. Pixels are tartined over the trace, pixels are not "unique position" on the canvas. Module 'N' recreates a B/W image. The threshold 'λ'is user trial/error from observing the Smath 'N' image. Though the B/W image 'N' looks thin, there is an immense amoount of duplicated 'X' that reflects the crappy original blue trace. Module Strip_X(data) cleans XY from 'X' duplicates/multiplicates. Module Ksmooth(j,X,Y)smooths the trace. On this low or not noisy XY data set it acts as an interpolation function. It would smooth a noisy XY. The 'XW' is now exploitable for further processing.

XY 343332484746512511616615614719718823822927926925103010291028212 mat :

data StripX nest stripped in 'R' u data 1 col : v data 2 col : k 0 : i 1 data rows 1 - (range u i 1 + el u i el - 0 ≠ R k k 1 + : el u i el v i el 12 mat : 11 line StripX done if 11 line for Un-nest R v R 1 el : j 2 R rows range v v R j el stack : for v 91 line :

This tool applies specifically to the "Digitiser" that produces lot of gray duplicates that must be removed for a usable data set, particularly if the project is followed by a Fourier spectrum, finite Diff's Deriv/CumulInt, any interpolation [linear, cubic]... The last entry [XY] is not accounted. To account for, stack terminator [0 0]

XY StripX 324651161471882292572 mat

t0 1 time :

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mat :

ideally, the digitizer should produce
same number of rows Y as there are cols
in 'Gray'. Even so, duplicates are produced
that must be further stripped  StripX(data) λ 166 : 11 sys

Digitize an image

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 Gray

N i 1 Gray rows range j 1 Gray cols range N i j el 0 Gray i j el λ ≤ 255 cases : for for N 21 line :

N N :

Gray cols 266

Digitizer [X,Y] r N rows : c N cols : k 1 : i 1 c range j 1 r range N j i el 1 ≤ X k el i : Y k el r j - : k k 1 + : 31 line No pixel if for for 41 line

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 N

XY X Y augment : xy XY StripX : 21 line

XY rows xy rows 21 mat 26619521 mat

XY 314151627284951071181210129131213111415141415201519162417291728172718341833232 mat

xy 314151627284951071181291311141415191624172718331937204021432246234924502550232 mat

1 time t0 - min 1.9

The Smath Gaussian 'ksmmooth'

ksmooth # plotG

xy char size clr plotG k 1 xy rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for xy r3 r4 r5 augment 21 line :

σ 0.3708158988058244 :

The Gaussian ksmooth

d K 12 π * sqrt σ * / d 2^2 σ 2^* / - exp * :

Smath recognises the silent 'bw', something
like the Mathcad "global definition". j X Y Ksmooth X i el X j el - bw / K Y i el * (i 1 X rows sum X i el X j el - bw / K (i 1 X rows sum / :

Gaussian Ksmooth Kernel

x K

X Y bw 13 mat

W j 1 X rows range s j el j X Y Ksmooth eval : for s 21 line :

W 11 mat

D [digitized]

D 31415162728495107118129131114141519162417271833193720402143224623492450255026492848294730463145324233413439353836373735383439344034423543364437453846394741484249445045514852515354545755615665577158765981608761926296631016410665111661176712368130691387014671151721567316074163751657616777170781737917680176821788317684175851748617087167881648916190159911569215493150941479514396139971359813199126100122101118102114103110104107105103106100107971089410990110881118511282113801147711575116721177011868119661206412163123601245912558126571275612855129541305313252133511345113650137501455014650148511495115152153531555415655157561595716158162591636016561167621686317064171651736617667179681806818568186681876818967190671936619565197641996320063201622036120560207592085821057211562135521554216532175321852220512225022449226482284723046231462334523544238432404224142243412444124740250392513925239255382563826137262371952 mat :

X D 1 col : Y D 2 col : 21 line

bw 5 : (bandwidth ≡ W W : (isolate W ≡ XW X W augment : 31 line

W 11 mat

The working path: collect & return [X,Y]=>[bw]=>[Ksmooth(j,X,Y,bw)]=>[W]=>[XW]

XW XW o 4 red plotG :

1 time t0 - min 5.7

D XW 2 1 sys Stem Construction Utility

Core component of the stem style P v replicate k 1 : i 1 v length range P i el 1 ≡ continue j 1 P i el range T k j + el v i el : for k k P i el + : 21 line if for T 31 line :

Stem construction vy stem N vy length : i 1 N range q i el 3 : q N el 2 : 21 line for 11 line i 1 N range v i el i : for i 1 N range S 3 i * el vy i el : for u q v replicate : V u S augment : V V 3 V rows 12 submatrix : 71 line :

clean spectrum chromatography from crappy web Spectrum W stem :

Spectrum

1 time t0 - min 5.7

Observe . . .

The X axis is anything from the crappy web source of the image.

More knowledge is necessary to affect some frequency. range.

You may want to decimate as well from the module below.

Decimation is a pre-requisite for fitting a model function.

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data n Decimate collect every 'n' pairs range 1 data rows n range : k 1 : i range u k el data i 1 el : v k el data i 2 el : k k 1 + : 31 line for u v augment 51 line :