vault backup: 2023-06-11 14:44:20
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!Załączniki/Op-Amp 2023-06-06 14.10.38.excalidraw.md
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!Załączniki/Op-Amp 2023-06-06 14.10.38.excalidraw.md
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---
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excalidraw-plugin: parsed
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tags: [excalidraw]
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---
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==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
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# Text Elements
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U wej
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^w5Tvp6uw
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U wyj
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^NxaltBnA
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Ur
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^CgcBtnee
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Ur = 0 gdy Ujemne sprzężenie zwrotne
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Ku=Uwyj/Uwej ^10jZNRX2
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%%
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# Drawing
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```compressed-json
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||||
```
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||||
%%
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@@ -1358,6 +1358,7 @@ Parametry
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Prądy
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||||
Punktacja
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Poprawnie
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Podaj
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obj
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oh
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oq
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ostrzegawczym
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operacyjny
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otwierający
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oznacza
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GoTo
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GS
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Gl
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@@ -6686,6 +6688,7 @@ energię
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elektryczną
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energii
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edge
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erroneous
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Length
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Link
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LN
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Js
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JX
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Bi
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Border
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Bh
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Bramki
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Barbara
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BlffqT
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Bandwidth
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Trans
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Type
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TF
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@@ -18756,6 +18764,7 @@ Transmitancja
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Tematy
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Taśmociągiem
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Taśmociąg
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Tvp
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Annots
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Annot
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Aac
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Synteza
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Significant
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Skośnie
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Signal
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Skrócone
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Rect
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Re
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Resources
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Niepewności
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Npięcia
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NVLKt
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Noise
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NxaltBnA
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ColorSpace
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Contents
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Cx
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Cewki
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Częstotliwość
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Całki
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Capacity
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Cecha
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CgcBtnee
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ExtGState
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Eu
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EV
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@@ -33294,6 +33310,8 @@ Dane
|
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Działanie
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||||
Digit
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Detale
|
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Dana
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Dany
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dA
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dET
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dg
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@@ -34693,6 +34711,9 @@ detal
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|
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|
||||
drzwi
|
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decyzji
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||||
dekodera
|
||||
decision
|
||||
YI
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||||
YT
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Yv
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@@ -37397,6 +37418,10 @@ charakterystyki
|
||||
częstotliwościowe
|
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cyfrowego
|
||||
czujnikiem
|
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cykliczny
|
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ciągi
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cyklicznych
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bI
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bx
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bM
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bezpamięciowego
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bipolarne
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będzie
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błędnej
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bitu
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błędy
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bitem
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jW
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je
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jz
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@@ -40065,6 +40094,7 @@ jednakowych
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jaką
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jomega
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jazdy
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jZNRX
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ac
|
||||
af
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ao
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@@ -46704,6 +46734,7 @@ Kodowanie
|
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KOEPF
|
||||
Kaskada
|
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Kształt
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Kodu
|
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IS
|
||||
ID
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||||
IQT
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równoległoboku
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równoległa
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rozmieszczone
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razy
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rozdzielnego
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tI
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tU
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ta
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@@ -54695,6 +54728,10 @@ wyznaczenia
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wykorzystano
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wykryją
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wykryciu
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wydłużony
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waga
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||||
wielomianu
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wej
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pDJ
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parenleftbigg
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parenrightbigg
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@@ -56153,6 +56190,14 @@ producent
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podaje
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pokozuje
|
||||
położenie
|
||||
przekłamania
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||||
pozycji
|
||||
podwójny
|
||||
parzystości
|
||||
parametrach
|
||||
podaj
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przykładowe
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pozycja
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||||
HD
|
||||
Ho
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Hg
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@@ -57392,6 +57437,8 @@ Hybrydowo
|
||||
Huffmana
|
||||
Hanoi
|
||||
Hazardy
|
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Haminga
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||||
Hamminga
|
||||
UDq
|
||||
Ue
|
||||
UV
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||||
@@ -58723,6 +58770,9 @@ Uob
|
||||
Uchyb
|
||||
UNDEFINED
|
||||
Utwórz
|
||||
Ujemne
|
||||
Uwyj
|
||||
Uwej
|
||||
yr
|
||||
yukC
|
||||
yF
|
||||
@@ -62713,6 +62763,7 @@ multimetru
|
||||
mierzącego
|
||||
mierzonego
|
||||
mocy
|
||||
macierz
|
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nD
|
||||
nF
|
||||
nZ
|
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@@ -64060,6 +64111,7 @@ narastające
|
||||
niepewność
|
||||
naszym
|
||||
następnie
|
||||
nierozdzielnego
|
||||
gNx
|
||||
gHI
|
||||
gri
|
||||
@@ -65401,6 +65453,8 @@ galwaniczna
|
||||
generuje
|
||||
gęstości
|
||||
gruby
|
||||
generującą
|
||||
generujący
|
||||
kXk
|
||||
kQ
|
||||
kx
|
||||
@@ -66799,6 +66853,7 @@ klasy
|
||||
kształcie
|
||||
krawędź
|
||||
krawędzi
|
||||
kodu
|
||||
üx
|
||||
ün
|
||||
ür
|
||||
@@ -69531,6 +69586,7 @@ zbocze
|
||||
zakresie
|
||||
zawsze
|
||||
założenia
|
||||
zwrotne
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ÜI
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Üj
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ÜX
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|
||||
"AiSD/AiSD.md",
|
||||
"TC/Wykład/8. Przerzutniki.md",
|
||||
@@ -234,19 +291,6 @@
|
||||
"AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 2.md",
|
||||
"AMiAL/!Materiały/calki_1.pdf",
|
||||
"AMiAL/AMiAL.md",
|
||||
"Elektrotechnika/Ćwiczenia/20230428101941.md",
|
||||
"!Załączniki/20230428101941 2023-04-28 10.39.09.excalidraw.md",
|
||||
"!Załączniki/20230428101941 2023-04-28 10.22.19.excalidraw.md",
|
||||
"AMiAL/Ćwiczenia/2 SEM/20230303081617.md",
|
||||
"EiM/EiM.md",
|
||||
"TC/Ćwiczenia/Untitled.md",
|
||||
"TC/Wykład/0. Wstęp.md",
|
||||
"TC/Wykład/Wykład.md",
|
||||
"TC/Ćwiczenia/1. Algebra Boola.md",
|
||||
"TC/Ćwiczenia/2. Realizacja układów na stykach.md",
|
||||
"TC/Ćwiczenia/3. Układy iteracyjne.md",
|
||||
"TC/Laboratorium/Laboratorium.md",
|
||||
"!Załączniki/2. Charakterystyki 2023-04-25 13.49.32.excalidraw.md",
|
||||
"!Załączniki/Recording 20230418135018.webm",
|
||||
"!Załączniki/Recording 20230418134959.webm",
|
||||
"EiM/Ćwiczenia",
|
||||
|
||||
6
EiM/Ćwiczenia/Op-Amp.md
Normal file
6
EiM/Ćwiczenia/Op-Amp.md
Normal file
@@ -0,0 +1,6 @@
|
||||
wzm w odwracającej
|
||||
nieodwracającej
|
||||
Wtórnika
|
||||
|
||||
|
||||
![[Op-Amp 2023-06-06 14.10.38.excalidraw]]
|
||||
@@ -1,5 +1,5 @@
|
||||
1100 1000 1110 1001 101 | 11
|
||||
Dane jest sekwencja. Zakładając że 19 symboli wystarcza do zapisania
|
||||
Dana jest sekwencja. Zakładając że 19 symboli wystarcza do zapisania
|
||||
Entropia w przypadku bezpamięciowego źródła:
|
||||
p0=9/19
|
||||
p1=10/19
|
||||
|
||||
136
TIiK/Ćwiczenia/3. Hamming.md
Normal file
136
TIiK/Ćwiczenia/3. Hamming.md
Normal file
@@ -0,0 +1,136 @@
|
||||
Podaj macierz generującą wydłużony kod Haminga (8,4)
|
||||
$H(8,4)$ $G=?$
|
||||
|
||||
$$\begin{gather}
|
||||
T=[P\ \ E]\\
|
||||
G=[E\ \ P^{T}]
|
||||
\end{gather}$$
|
||||
$n=8,\ k=4$
|
||||
$m=n-k=4$
|
||||
$n=1;2;3;8$
|
||||
|
||||
$$T= \begin{bmatrix}
|
||||
1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1
|
||||
\end{bmatrix}
|
||||
$$
|
||||
$w_{1}=w_{3}\oplus w_{5} \oplus w_{7}$
|
||||
$w_{2}=w_{3}\oplus w_{6} \oplus w_{7}$
|
||||
$w_{4}=w_{5}\oplus w_{6} \oplus w_{7}$
|
||||
$w_{8}=\oplus\sum w_{n}$
|
||||
|
||||
$n=1_{10}=0001_{2}$
|
||||
$\overline{w_{1}}= 1101001$
|
||||
|
||||
$n=2_{10}=0010_{2}$
|
||||
$\overline{w_{2}}=01010101$
|
||||
|
||||
$n=4_{10}=0100_{2}$
|
||||
$\overline{w_{4}}=10011001$
|
||||
|
||||
$n=8_{10}=1000_{2}$
|
||||
$\overline{w_{8}}=11100001$
|
||||
|
||||
$$G= \begin{bmatrix}
|
||||
\overline{w_{8}} \\ \overline{w_{4}} \\ \overline{w_{2}} \\ \overline{w_{1}} \\
|
||||
\end{bmatrix}=\begin{bmatrix}
|
||||
1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \\ 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0
|
||||
\end{bmatrix}$$
|
||||
|
||||
$n=6_{10}=0110_{2}$
|
||||
$$\overline{w_{6}}=n\cdot G= \begin{bmatrix}0 & 1 & 1 & 0\end{bmatrix}\begin{bmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \\ 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0\end{bmatrix}=11001100$$
|
||||
|
||||
$\overline{w_{7}}=\begin{bmatrix}0 & 1 & 1 & 1\end{bmatrix}G=00011110$
|
||||
|
||||
$\overline{w_{13}}=\begin{bmatrix}1 & 1 & 0 & 1\end{bmatrix}G=10101010$
|
||||
|
||||
|
||||
|
||||
|
||||
## Oblicz prawdopodobieństwo błędnej decyzji dekodera kodu Hamminga (7,4) jeżeli prawdopodobieństwo przekłamania bitu wynosi $10^{-3}$, błędy są niezależne.
|
||||
ed = erroneous decision
|
||||
|
||||
|
||||
$H(7,4)$ $p=10^{-3}$
|
||||
$P_{OK}=(0.999)^{7}=(1-p)^{7}$
|
||||
$P_{e1}=(^{7}_{1})p^{1}\cdot (1-p)^{6}=7\cdot 10^{-3} \cdot (0.999)^{6}\approx 1$
|
||||
$P_{ed}=1-P_{OK}-P_{e1}=P_{e2}+\dots+P_{e7}$
|
||||
$P_{ed}\approx P_{e2}=(^7_2)=p^2(1-p)^5=\frac{7!}{2!5!}10^{-6}\cdot(0.999)^5=21\cdot 10^{-6}\cdot(0.999)^5\approx21\cdot 10^{-6}$
|
||||
|
||||
|
||||
$H(8,4)$ $p=10^{-3}$
|
||||
$P_{OK}=(1-p)^{8}\approx 0.992$
|
||||
$P_{e1}=(^{8}_{1})p^{1}(1-p)^{7}\approx 0.008$
|
||||
$P_{ed}=1-P_{OK}-P_{e1}-P_{e2}\approx 56\cdot 10^{-9}$
|
||||
|
||||
|
||||
## Skrócone:
|
||||
$s.k.H(6,3)$
|
||||
$n=6$, ale syndrom $\in\left<0;7\right)$, co oznacza błąd na "7" pozycji.
|
||||
Błąd podwójny, ale tylko 1 z $\left(^{6}_{2}\right)$
|
||||
|
||||
$P_{ed}=\left[\left(^{6}_{2}\right)-1\right]p^{2}(1-p)^{4}+P_{e3}+P_{e4}+\dots\approx14\cdot 10^{-6}$
|
||||
|
||||
## Dany jest kod z bitem parzystości o parametrach (8,7)
|
||||
|
||||
m=1
|
||||
$P_{ed}=\sum\limits_{n=1}^{n+1} P_{en}\approx28\cdot10^{-6}$
|
||||
|
||||
|
||||
$h=101_{2}$
|
||||
$g=1101_{2}$
|
||||
$$\begin{gather}
|
||||
h\cdot g = 1101\cdot 101=111001
|
||||
\end{gather}$$
|
||||
---
|
||||
$$\begin{gather}
|
||||
h(x)=x^{2}+1\\
|
||||
g(x)=x^{3}+x^{2}+1
|
||||
|
||||
h(x)g(x)=(x^{2}+1)(x^{3}+x^{2}+1)=x^{5}+x^{4}+x^{3}+x^{0}= 111001
|
||||
|
||||
\end{gather}
|
||||
|
||||
$$
|
||||
|
||||
## Dany jest wielomian generujący $g(x)=x^3+x+1$, który generuje kod cykliczny o parametrach (7,4). Podaj macierz generującą i podaj przykładowe ciągi dla
|
||||
### Kodu cyklicznego nierozdzielnego
|
||||
$$\begin{gather}
|
||||
w(x)=h(x)\cdot g(x)\\
|
||||
\\
|
||||
h=3_{10}=0011_{2}\\
|
||||
h(x)=x\oplus1\\
|
||||
\overline{w_{3}}(x)=(x\oplus1)(x^{3}\oplus x\oplus 1)=x^{4}\oplus x^{3} \oplus x^{2} \oplus 1 = 00\|11101
|
||||
\\
|
||||
\\
|
||||
1011\cdot 0011=0011101
|
||||
\\
|
||||
\\
|
||||
\\
|
||||
\overline{w_{1}}= 0001011\\
|
||||
\overline{w_{2}}= 0010110\\
|
||||
\overline{w_{4}}= 0101100\\
|
||||
\overline{w_{8}}= 1011000\\
|
||||
|
||||
|
||||
G=\begin{bmatrix}
|
||||
w_{8} \\ w_{4} \\ w_{2} \\ w_{1}
|
||||
\end{bmatrix}\cdot \begin{bmatrix}
|
||||
1 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1
|
||||
\end{bmatrix}
|
||||
\\
|
||||
\overline{w_{14}}=[1110]G=1100010
|
||||
|
||||
\end{gather}$$
|
||||
Minimalna waga = 3 → $d_{min}=3$
|
||||
Cecha kodów cyklicznych to shiftowanie słowa w lewo - g(x) razy pozycja w formie wielomianu
|
||||
|
||||
### Kodu cyklicznego rozdzielnego
|
||||
$g(x)=x^3 +x +1$
|
||||
|
||||
$$
|
||||
\begin{gather}
|
||||
w(x)=x^{k-1}\cdot h(x)+r(x)\\
|
||||
r(x)=x^{k-1}\cdot h(x)\mod{g(x)}
|
||||
|
||||
\end{gather}
|
||||
$$
|
||||
Reference in New Issue
Block a user