381616b6-033a-482a-9378-943e76f86619 30 15 12 decimal

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

Z transform of the sequence 's'

local definition z X 2 n -^z n^/ n 015 sum 11 line :

saniy MCD 5 X 1.11111111111111

x X

n 015 range :

s 2 n -^vectorize :

s 4 el 0.125

s 1 0.5 0.25 0.125 0.0625 0.03125 0.015625 0.0078125 0.00390625 0.001953125 0.0009765625 0.00048828125 0.000244140625 0.0001220703125 0.00006103515625 0.000030517578125 161 mat

r 2 :

The inverse transform recovers original sequence n X T r n 1 -^2 π * / r i θ * exp * X n 1 - (θ * i * exp * θ 02 π * int * abs :

sanity MCD 4 X T 0.125

idx 1 s rows range :

idx s augment

user sanity j 6 :

s j el j X T 21 mat 0.03125 0.03125 21 mat

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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f x 0.5 + x 2^x - 0.5 + / x x 1 - / (* :

f parfrac x convert maple 3 x 1 - / 3 - 4 x * + 2 x 2^* 2 x * - 1 + / -

n Clear 1

z z π - / z n invztrans maple π n^