XY raw data [100]

f359a89a-8dd1-489e-a740-4ff465543d40 16 4 5 decimal

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

XY raw data [100]

XY 0.5 - 0.105 0.48 - 0.115 0.46 - 0.126 0.44 - 0.138 0.42 - 0.151 0.4 - 0.165 0.38 - 0.181 0.36 - 0.198 0.34 - 0.217 0.32 - 0.238 0.3 - 0.261 0.28 - 0.286 0.26 - 0.313 0.24 - 0.343 0.22 - 0.375 0.2 - 0.411 0.18 - 0.45 0.16 - 0.493 0.14 - 0.539 0.12 - 0.59 0.1 - 0.645 0.08 - 0.705 0.06 - 0.77 0.04 - 0.841 0.02 - 0.918 01 0.02 1.09 0.04 1.186 0.06 1.288 0.08 1.398 0.1 1.515 0.12 1.638 0.14 1.767 0.16 1.902 0.18 2.043 0.2 2.186 0.22 2.333 0.24 2.48 0.26 2.627 0.28 2.773 0.3 2.914 0.32 3.05 0.34 3.18 0.36 3.326 0.38 3.415 0.4 3.52 0.42 3.62 0.44 3.73 0.46 3.78 0.48 3.848 0.5 3.903 0.52 3.971 0.54 4.023 0.56 4.072 0.58 4.117 0.6 4.16 0.62 4.178 0.64 4.208 0.66 4.235 0.68 4.259 0.7 4.281 0.72 4.301 0.74 4.319 0.76 4.338 0.78 4.351 0.8 4.362 0.82 4.377 0.84 4.387 0.86 4.4 0.88 4.407 0.9 4.419 0.92 4.424 0.94 4.436 0.96 4.444 0.98 4.451 1 4.457 1.02 4.463 1.04 4.468 1.06 4.475 1.08 4.48 1.1 4.484 1.12 4.489 1.14 4.493 1.16 4.497 1.18 4.501 1.2 4.505 1.22 4.508 1.24 4.511 1.26 4.513 1.28 4.518 1.3 4.52 1.32 4.523 1.34 4.525 1.36 4.527 1.38 4.531 1.4 4.533 1.42 4.535 1.44 4.537 1.46 4.539 1.48 4.54 1002 mat :

σ 0.3708158988058244 :

The Gaussian ksmooth

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

Smath recognises the silent 'bw', something
like the Mathcad "global definition". W 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 / : j 1 X rows range s j el j X Y Ksmooth eval : for s 31 line :

Gaussian Ksmooth Kernel

x K

X Y bw 13 mat

Derivatives [FD, convolution]

Finite differences "FD" derivative of data set data D X data 1 col : Y data 2 col : n X rows : deriv 1 el 0 : deriv n el 0 : i 2 n 1 - (range deriv i el 0.5 Y i 1 + el Y i el - X i 1 + el X i el - / Y i el Y i 1 - el - X i el X i 1 - el - / + (* : for deriv 1 el deriv 2 el : deriv n el deriv deriv rows el : X deriv augment 91 line :

Derivative convolution data Δeriv Vx data 1 col : Vy data 2 col : dx Vx 2 el Vx 1 el - : scale 1 - 2 dx * / : f 1 - 0113 mat transpose : Dy Vy f al_convr1d : Dy Dy 2 Dy rows 1 - 11 submatrix : Deriv Vx scale Dy * augment : Deriv Deriv 2 Deriv rows 1 - 12 submatrix : 91 line :

X XY 1 col : Y XY 2 col : bw 0.15 : (bandwidth ≡ XW X W augment : 41 line

Sanity smoothed derivative ... XW is the smoothed XY

XY Δeriv XW Δeriv 2 1 sys

[W]

FD derivative and convolution derivative
are strictly = ... convolution is short 
of the 1rst and last point. subX X 29911 submatrix : subD XW D 29912 submatrix : Δelta subD 2 col XW Δeriv 2 col - : compare subX Δelta augment : 41 sys

Explain Project:

We are given a data set to quality control. Though it loks good, it is

noisy and unfit for publishing. The Gaussian ksmooth reveals an

excellent candidate. That it shows decrease in amplitude is not

detrimental, considering the poor data collection. The discrete

derivative is a noise amplifier. XW is the smoothed data set.

we can fit a model function for this particular one [not offered].

]]>