0c821dec-71ae-477e-97e0-1c9d854d4f2b 6 15 12 decimal

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

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1. WinGrab captured an 84x84 piece of Smath w/o grid 2. crop image, copy/paste in IrfanView, contrast and else 3. saved in file [as *.PNG or else supporting translucent] 4. Insert background, browse, fit ... done

Maths over translucent background

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

x c 11 x ≤ (x 16 ≤ (& cases :

x ch 10 x ≤ (x 16 ≤ (& cases :

n 116 range :

r 2 :

z H z 0.5 + z 2^z - 0.5 + / :

H(z) under unit discrete impulse
Y(z) algo input to  ... Inv(n,Y) z Y z 0.5 + z 2^z - 0.5 + / (z z 1 - / (* :

3 appVersion 0.98.6179 ≡

0 H 1

The inverse Z_transform in the discrete domain n Y Inv r n^2 π * / r i θ * exp * Y n θ * i * exp * θ 02 π * int * :

j 1 n rows range y j el n j el Y Inv : for

R n y abs vectorize augment : Z R . 14 red plot : 21 sys

1/1 sanity Mathcad source code

x H x ch * Z 2 1 sys

Z_system for inverse transform

x H x Y x c * 2 1 sys

R 112 2.5 3 3.5 4 3.75 5 3.5 6 3.125 7 2.875 8 2.813 9 2.875 10 2.969 11 3.031 12 3.047 13 3.031 14 3.008 15 2.992 16 2.988 162 mat

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