HEADmaster

29 files changed, 3429 insertions, 19 deletions

diff --git a/tabor/delavnica/manim/anim.py b/tabor/delavnica/manim/anim.py
new file mode 100644
index 0000000..eaac687
--- /dev/null
+++ b/tabor/delavnica/manim/anim.py
@@ -0,0 +1,13 @@
+
+from manim import *
+# or: from manimlib import *
+# from manim_slides import Slide
+
+class Test(Scene):
+	def construct(self):
+		circle = Circle(radius=3, color=BLUE)
+		dot = Dot()
+
+		self.play(MoveAlongPath(dot, circle), run_time=2, rate_func=linear)
+
+		self.play(dot.animate.move_to(ORIGIN))
diff --git a/tabor/delavnica/manim/example.py b/tabor/delavnica/manim/example.py
deleted file mode 100644
index 8356367..0000000
--- a/tabor/delavnica/manim/example.py
+++ /dev/null
@@ -1,19 +0,0 @@
-
-from manim import *
-# or: from manimlib import *
-from manim_slides import Slide
-
-class BasicExample(Slide):
-    def construct(self):
-        circle = Circle(radius=3, color=BLUE)
-        dot = Dot()
-
-        self.play(GrowFromCenter(circle))
-        self.next_slide()  # Waits user to press continue to go to the next slide
-
-        self.start_loop()  # Start loop
-        self.play(MoveAlongPath(dot, circle), run_time=2, rate_func=linear)
-        self.end_loop()  # This will loop until user inputs a key
-
-        self.play(dot.animate.move_to(ORIGIN))
-        self.next_slide()  # Waits user to press continue to go to the next slide
diff --git a/tabor/delavnica/manim/predst.py b/tabor/delavnica/manim/predst.py
new file mode 100644
index 0000000..7096bd3
--- /dev/null
+++ b/tabor/delavnica/manim/predst.py
@@ -0,0 +1,35 @@
+
+from manim import *
+# or: from manimlib import *
+from manim_slides import Slide
+
+class Predst(Slide):
+	def construct(self):
+		title = VGroup(
+			Text("Fourierova transformacija", t2c={"Fourierova": BLUE}),
+			Text("Predavanje na naravoslovnem taboru Gimnazije Bežigrad", font_size=32, t2c={"naravoslovnem": GREEN}),
+			Text("Anton Luka Šijanec in Vasja Žorž", font_size=32, t2c={"Šijanec": YELLOW, "Žorž": YELLOW}),
+			Text("Medvedje Brdo, 24. junija 2023", font_size=32, t2c={"junija": RED})
+		).arrange(DOWN)
+		self.play(FadeIn(title))
+		self.next_slide() # --------------------------------------------
+		self.clear()
+		besedilo = VGroup(
+			Text("Splošno"),
+			BulletedList("")
+		).arrange(DOWN)
+		self.play(besedilo)
+		self.next_slide() # --------------------------------------------
+		self.clear()
+		circle = Circle(radius=3, color=BLUE)
+		dot = Dot()
+
+		self.play(GrowFromCenter(circle))
+		self.next_slide()  # Waits user to press continue to go to the next slide
+
+		self.start_loop()  # Start loop
+		self.play(MoveAlongPath(dot, circle), run_time=2, rate_func=linear)
+		self.end_loop()  # This will loop until user inputs a key
+
+		self.play(dot.animate.move_to(ORIGIN))
+		self.next_slide()  # Waits user to press continue to go to the next slide
diff --git a/tabor/delavnica/manim/sobota.md b/tabor/delavnica/manim/sobota.md
new file mode 100644
index 0000000..3347f9c
--- /dev/null
+++ b/tabor/delavnica/manim/sobota.md
@@ -0,0 +1,85 @@
+fourierova transformacija
+=========================
+
+# motivacija
+
+* vizualizacija zvoka s spektrogramom
+* frekvenčni spekter zvoka je jakost zvoka v odvisnosti od posamezne frekvence zvoka
+* zvok dobimo kot amplitudo v odvisnosti od časa, spektrogram pa je grafični prikaz spremembe frekvenčnega spektra skozi čas
+* kako torej razstavimo vhodni signal (trenutna amplituda v odvisnosti od časa) v frekvenčni spekter
+
+# motivacija 2
+
+* plimovanje sicer na prvi pogled izgleda naključno, vendar se izkaže, da gre za vsoto sinusnih valovanj, ki jih povzročajo spreminjajoče se lokacije nebesnih teles (razdalje do Zemlje) z različnimi amplitudami, faznimi zamiki in frekvencami.
+* napovedovanje bi torej izvedli tako, da bi našli te komponente, ki sestavljajo ...
+
+# definicija pojmov
+
+* kaj je sinus, kosinus
+* kaj je valovanje:
+    * kaj je amplituda
+    * kaj je faza, fazni zasuk
+    * kaj je frekvenca
+    * primeri: zvok, ...
+* kompleksno število in kompleksna ravnina
+
+# fourierova vrsta
+
+* vsota končno oz. neskončno mnogo kosinusnih valovanj z različnimi amplitudami, frekvencami in faznimi zamiki
+* kako bi zapisali npr. kvadratno valovanje (square wave) kot fourierovo vrsto ... sawtooth wave, triangl.
+* vse periodične funkcije lahko zapišemo s fourierovo vrsto, vendar ne vedno končno
+* enostavno je sešteti periodične funkcije, težje pa je ugotoviti, katere seštete periodične funkcije so komponente nekega danega valovanja/signala.
+
+# fourierova transformacija
+
+* matematična operacija, ki vhodnim podatkom v obliki amplitude v odvisnosti od časa priredi razporeditev frekvenčnih komponent, ki predstavljajo te vhodne podatke ter amplitude posameznih frekvenc.
+
+# intuicija za delovanje fourierove transformacije
+
+* animacija: *navijanje* nihanja po enotski krožnici; ko periodo zadenemo z obsegom kroga.
+* kako izgleda sum sinx in sin2x
+* obnašanje faznega zasuka signala oz. komponente
+* transformacija vsote dveh signalov je enaka vsoti transformacij posameznih komponent obeh signalov: ft(a(x)+b(x))=ft(a(x))+ft(b(x))
+
+# matematična oblika
+
+* eulerjeva formula: e^(i\phi)=cos\phi+isin\phi
+    * ... izpeljava
+* inverz je fourierova 
+
+# diskretni signal
+
+* za razliko od zveze reprezentacije valovanja, je diskretna reprezentacija signala samo zaporedje vzorcev amplitude na časovni interval.
+* ko nek signal zajemamo, so v diskretni obliki, torej imamo zaporedje vzorcev (samplov) amplitude v odvisnosti od odvisne spremenljivke (časa)
+    * primer: mikrofon, ...
+* kako pa na takih podatkih izvesti fourierovo transformacijo in pridobiti frekvenčne komponente, ki sestavljajo signal
+    * mat zapis zaporedja a_n
+* teorija nyquist-shannon: za popolno reprezentacijo signala z največjo frekvenco B potrebujemo vsaj 1/(2B) časovnega razmika med posameznimi vzorci (frekvenca vzorčenja je 2B)
+    * pojasni!
+    * slikica aliasing
+
+# dft
+
+* poleg vhoda je tudi izhod dft je diskreten, s tem da imamo vrednosti amplitud diskretnih frekvenčnih komponent -- izračunamo končno mnogo frekvenčnih komponent, kolikor jih potrebujemo (ločljivost)
+* koncept transformacijskega okna -- lahko so to vsi vzorci (recimo pri frekvenčnem spektru), lahko pa je to le del zaporednih vzorcev (recimo pri spektrogramu)
+* algoritem: naivno bi za vsako željeno frekvenco izračunali amplitudo, torej tak sum: sum začenjši t=t_1 do t_n A_vhodni(t) * e^(i2\pi f t)
+* izračunska kompleksnost algoritma je število, ki predstavlja število korakov glede na število vhodnih podatkov:
+    * v tem naivnem primeru algoritma za izračun: O(n * m), kjer je n število željenih frekvenc in m število vzorcev v oknu
+
+# hitra diskretna transformacija
+
+* nekatera
+* zmanjša izračunsko zahtevnost na
+
+# praktične uporabe
+
+* kompresija slik z izgubami -- JPEG
+* dtmf z diskretno ft
+
+# dopplerjev radar
+
+# uvod v heisenbergovo načelo nedoločnosti
+
+# misc
+
+* https://prajwalsouza.github.io/Experiments/Fourier-Transform-Visualization.html
diff --git a/tabor/delavnica/odp/Accordion_registers.ogg b/tabor/delavnica/odp/Accordion_registers.ogg
new file mode 100644
index 0000000..683ea2e
--- /dev/null
+++ b/tabor/delavnica/odp/Accordion_registers.ogg
diff --git a/tabor/delavnica/odp/Accordion_registers.png b/tabor/delavnica/odp/Accordion_registers.png
new file mode 100644
index 0000000..44cc312
--- /dev/null
+++ b/tabor/delavnica/odp/Accordion_registers.png
diff --git a/tabor/delavnica/odp/predst.odp b/tabor/delavnica/odp/predst.odp
new file mode 100644
index 0000000..1ef1975
--- /dev/null
+++ b/tabor/delavnica/odp/predst.odp
diff --git a/tabor/delavnica/predst/bt.png b/tabor/delavnica/predst/bt.png
new file mode 100644
index 0000000..6cbba8e
--- /dev/null
+++ b/tabor/delavnica/predst/bt.png
diff --git a/tabor/delavnica/predst/doppler.png b/tabor/delavnica/predst/doppler.png
new file mode 100644
index 0000000..4ddbc8c
--- /dev/null
+++ b/tabor/delavnica/predst/doppler.png
diff --git a/tabor/delavnica/predst/dtmf.png b/tabor/delavnica/predst/dtmf.png
new file mode 100644
index 0000000..00a6915
--- /dev/null
+++ b/tabor/delavnica/predst/dtmf.png
diff --git a/tabor/delavnica/predst/dtmffreq.png b/tabor/delavnica/predst/dtmffreq.png
new file mode 100644
index 0000000..f992265
--- /dev/null
+++ b/tabor/delavnica/predst/dtmffreq.png
diff --git a/tabor/delavnica/predst/film.mp4 b/tabor/delavnica/predst/film.mp4
new file mode 100644
index 0000000..37ad5de
--- /dev/null
+++ b/tabor/delavnica/predst/film.mp4
diff --git a/tabor/delavnica/predst/nyquistshannon.png b/tabor/delavnica/predst/nyquistshannon.png
new file mode 100644
index 0000000..503d354
--- /dev/null
+++ b/tabor/delavnica/predst/nyquistshannon.png
diff --git a/tabor/delavnica/predst/predstavitev.lyx b/tabor/delavnica/predst/predstavitev.lyx
new file mode 100644
index 0000000..4e49773
--- /dev/null
+++ b/tabor/delavnica/predst/predstavitev.lyx
@@ -0,0 +1,3275 @@
+#LyX 2.3 created this file. For more info see http://www.lyx.org/
+\lyxformat 544
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass beamer
+\begin_preamble
+\usepackage[
+    type={CC},
+    modifier={by-sa},
+    version={3.0},
+]{doclicense}
+
+\usepackage{bera}% optional: just to have a nice mono-spaced font
+\usepackage{listings}
+\usepackage{xcolor}
+\lstset{
+	extendedchars=true,
+	literate={č}{{\v{c}}}1 {ž}{{\v{z}}}1 {š}{{\v{s}}}1,
+}
+
+\colorlet{punct}{red!60!black}
+\definecolor{background}{HTML}{EEEEEE}
+\definecolor{delim}{RGB}{20,105,176}
+\colorlet{numb}{magenta!60!black}
+
+\lstdefinelanguage{json}{
+    basicstyle=\normalfont\ttfamily,
+    numbers=left,
+    numberstyle=\scriptsize,
+    stepnumber=1,
+    numbersep=8pt,
+    showstringspaces=false,
+    breaklines=true,
+    frame=lines,
+    backgroundcolor=\color{background},
+    literate=
+     *{0}{{{\color{numb}0}}}{1}
+      {1}{{{\color{numb}1}}}{1}
+      {2}{{{\color{numb}2}}}{1}
+      {3}{{{\color{numb}3}}}{1}
+      {4}{{{\color{numb}4}}}{1}
+      {5}{{{\color{numb}5}}}{1}
+      {6}{{{\color{numb}6}}}{1}
+      {7}{{{\color{numb}7}}}{1}
+      {8}{{{\color{numb}8}}}{1}
+      {9}{{{\color{numb}9}}}{1}
+      {:}{{{\color{punct}{:}}}}{1}
+      {,}{{{\color{punct}{,}}}}{1}
+      {\{}{{{\color{delim}{\{}}}}{1}
+      {\}}{{{\color{delim}{\}}}}}{1}
+      {[}{{{\color{delim}{[}}}}{1}
+      {]}{{{\color{delim}{]}}}}{1},
+}
+
+
+
+
+
+
+
+\usetheme{Warsaw}
+% or ...
+
+\setbeamercovered{transparent}
+% or whatever (possibly just delete it)
+\usepackage{multimedia}
+
+\usetheme{Warsaw}
+
+\setbeamercolor{normal text}{fg=white,bg=black!90}
+\setbeamercolor{structure}{fg=white}
+
+\setbeamercolor{alerted text}{fg=red!85!black}
+
+\setbeamercolor{item projected}{use=item,fg=black,bg=item.fg!35}
+
+\setbeamercolor*{palette primary}{use=structure,fg=structure.fg}
+\setbeamercolor*{palette secondary}{use=structure,fg=structure.fg!95!black}
+\setbeamercolor*{palette tertiary}{use=structure,fg=structure.fg!90!black}
+\setbeamercolor*{palette quaternary}{use=structure,fg=structure.fg!95!black,bg=black!80}
+
+\setbeamercolor*{framesubtitle}{fg=white}
+
+\setbeamercolor*{block title}{parent=structure,bg=black!60}
+\setbeamercolor*{block body}{fg=black,bg=black!10}
+\setbeamercolor*{block title alerted}{parent=alerted text,bg=black!15}
+\setbeamercolor*{block title example}{parent=example text,bg=black!15}
+\usepackage{multicol}
+\usepackage{listings}
+\usepackage{siunitx}
+\end_preamble
+\options aspectratio=169
+\use_default_options false
+\maintain_unincluded_children false
+\language slovene
+\language_package default
+\inputencoding utf8-plain
+\fontencoding global
+\font_roman "lmodern" "default"
+\font_sans "lmss" "default"
+\font_typewriter "lmtt" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures false
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_package amsmath 2
+\use_package amssymb 2
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 0
+\use_minted 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 2
+\tocdepth 2
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style german
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+This file is a solution template for:
+\end_layout
+
+\begin_layout Itemize
+Talk at a conference/colloquium.
+ 
+\end_layout
+
+\begin_layout Itemize
+Talk length is about 20min.
+ 
+\end_layout
+
+\begin_layout Itemize
+Style is ornate.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+Copyright 2004 by Till Tantau <tantau@users.sourceforge.net>.
+ 
+\end_layout
+
+\begin_layout Plain Layout
+In principle, this file can be redistributed and/or modified under the terms
+ of the GNU Public License, version 2.
+ However, this file is supposed to be a template to be modified for your
+ own needs.
+ For this reason, if you use this file as a template and not specifically
+ distribute it as part of a another package/program, the author grants the
+ extra permission to freely copy and modify this file as you see fit and
+ even to delete this copyright notice.
+ 
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Title
+Fourierova transformacija
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+Fourierova transformacija
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subtitle
+Predavanje na naravoslovnem taboru
+\end_layout
+
+\begin_layout Author
+Vasja Žorž
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset Flex InstituteMark
+status open
+
+\begin_layout Plain Layout
+1
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+and
+\end_layout
+
+\end_inset
+
+ Anton Luka Šijanec
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+\begin_inset Flex InstituteMark
+status collapsed
+
+\begin_layout Plain Layout
+2
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Itemize
+Give the names in the same order as the appear in the paper.
+\end_layout
+
+\begin_layout Itemize
+Use the 
+\begin_inset Quotes eld
+\end_inset
+
+Institute mark
+\begin_inset Quotes erd
+\end_inset
+
+ inset (
+\family sans
+Insert\SpecialChar menuseparator
+Custom Insets\SpecialChar menuseparator
+InstituteMark
+\family default
+) only if the authors have different affiliations.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+Vasja Žorž
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+and
+\end_layout
+
+\end_inset
+
+ Anton Luka Šijanec
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+- optional, use only with lots of authors
+\end_layout
+
+\begin_layout Plain Layout
+- if there are really lots of authors, use 
+\begin_inset Quotes eld
+\end_inset
+
+Author et al.
+\begin_inset Quotes erd
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Institute
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+\begin_inset Flex InstituteMark
+status collapsed
+
+\begin_layout Plain Layout
+1
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+Mentor: xxx 
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+and
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ Gimnazija Bežigrad
+\begin_inset Newline newline
+\end_inset
+
+Medvedje Brdo
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+\begin_inset Flex InstituteMark
+status collapsed
+
+\begin_layout Plain Layout
+2
+\end_layout
+
+\end_inset
+
+Department of Theoretical Philosophy
+\begin_inset Newline newline
+\end_inset
+
+University of Elsewhere
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Itemize
+Use the 
+\begin_inset Quotes eld
+\end_inset
+
+Institute mark
+\begin_inset Quotes erd
+\end_inset
+
+ inset (
+\family sans
+Insert\SpecialChar menuseparator
+Custom Insets\SpecialChar menuseparator
+InstituteMark
+\family default
+) only if there are several affiliations.
+\end_layout
+
+\begin_layout Itemize
+Keep it simple, no one is interested in your street address.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+Gimnazija Bežigrad
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+optional, but mostly needed
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Date
+V sredo, 28.
+ junija 2023
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Itemize
+Either use conference name or its abbreviation.
+ 
+\end_layout
+
+\begin_layout Itemize
+Not really informative to the audience, more for people (including yourself)
+ who are reading the slides online
+\end_layout
+
+\end_inset
+
+
+\begin_inset Argument 1
+status open
+
+\begin_layout Plain Layout
+28.
+ maja 2023
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+optional, should be abbreviation of conference name
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+If you have a file called "institution-logo-filename.xxx", where xxx is a
+ graphic format that can be processed by latex or pdflatex, resp., then you
+ can add a logo by uncommenting the following:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+%
+\backslash
+pgfdeclareimage[height=0.5cm]{institution-logo}{institution-logo-filename}
+\end_layout
+
+\begin_layout Plain Layout
+
+%
+\backslash
+logo{
+\backslash
+pgfuseimage{institution-logo}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The following causes the table of contents to be shown at the beginning
+ of every subsection.
+ Delete this, if you do not want it.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+%
+\backslash
+AtBeginSubsection[]{% enejble to inflate
+\end_layout
+
+\begin_layout Plain Layout
+
+%  
+\backslash
+frame<beamer>{ 
+\end_layout
+
+\begin_layout Plain Layout
+
+%    
+\backslash
+frametitle{Pregled vsebine}   
+\end_layout
+
+\begin_layout Plain Layout
+
+%
+\backslash
+tableofcontents[currentsection, currentsubsection] 
+\end_layout
+
+\begin_layout Plain Layout
+
+%  }
+\end_layout
+
+\begin_layout Plain Layout
+
+%}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+If you wish to uncover everything in a step-wise fashion, uncomment the
+ following command:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+%
+\backslash
+beamerdefaultoverlayspecification{<+->}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Pregled vsebine
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout Plain Layout
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{multicols}{2}
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset toc
+LatexCommand tableofcontents
+
+\end_inset
+
+
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{multicols}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+Structuring a talk is a difficult task and the following structure may not
+ be suitable.
+ Here are some rules that apply for this solution:
+\end_layout
+
+\begin_layout Itemize
+Exactly two or three sections (other than the summary).
+\end_layout
+
+\begin_layout Itemize
+At *most* three subsections per section.
+\end_layout
+
+\begin_layout Itemize
+Talk about 30s to 2min per frame.
+ So there should be between about 15 and 30 frames, all told.
+\end_layout
+
+\begin_layout Itemize
+A conference audience is likely to know very little of what you are going
+ to talk about.
+ So *simplify*!
+\end_layout
+
+\begin_layout Itemize
+In a 20min talk, getting the main ideas across is hard enough.
+ Leave out details, even if it means being less precise than you think necessary.
+\end_layout
+
+\begin_layout Itemize
+If you omit details that are vital to the proof/implementation, just say
+ so once.
+ Everybody will be happy with that.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Uvod
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Motivacija
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename waveform.png
+	width 100text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Zvočni signal posnetka glasbenega inštrumenta
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Uvod
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Motivacija
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename spekter.png
+	width 100text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Frekvenčni spekter periodičnega signala
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Uvod
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Motivacija: Plimovanje
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename tideforces.jpg
+	width 40text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Višina gladine morja kot posledica vplivov nebesnih teles
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Uvod
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Motivacija: Plimovanje
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename tidalsum.gif
+	width 40text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Valovne komponente, ki se sestavijo v plimovanje
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Osnovni matematični pojmi
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Valovanje
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+\begin_inset Formula $\lambda$
+\end_inset
+
+, 
+\begin_inset Formula $t_{0},$
+\end_inset
+
+
+\begin_inset Formula $\nu$
+\end_inset
+
+, 
+\begin_inset Formula $\omega$
+\end_inset
+
+, 
+\begin_inset Formula $k$
+\end_inset
+
+, 
+\begin_inset Formula $\phi$
+\end_inset
+
+, 
+\begin_inset Formula $A$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $f(x)=A\cdot\cos(\omega t-kx+\phi)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\omega=2\pi\nu$
+\end_inset
+
+, 
+\begin_inset Formula $\nu=1/t_{0}$
+\end_inset
+
+, 
+\begin_inset Formula $k=2\pi/\lambda$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+primeri valovanja: zvok, svetloba, izmenični tok, potresni valovi, plimovanje
+\begin_inset Note Note
+status open
+
+\begin_layout Itemize
+https://www.desmos.com/calculator/ptxc1dutf9
+\end_layout
+
+\begin_layout Itemize
+vprašanja: itd
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Osnovni matematični pojmi
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Množica 
+\begin_inset Formula $\mathbb{C}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+imaginarna enota: 
+\begin_inset Formula $i^{2}+1=0$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+imaginarna enota je definirano kot takšno število, ki reši to enačbo za
+ i
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\mathbb{C}\coloneqq\{a+bi;\ a,b\in\mathbb{R}\}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+množico kompleksnih števil lahko ponazorimo s kompleksno ravnino
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+nariševa jo na tablo, poveva operacije v C
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Osnovni matematični pojmi
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Eulerjeva formula
+\end_layout
+
+\begin_layout Itemize
+polarni zapis kompleksnega števila: 
+\begin_inset Formula $r\cdot e^{i\theta}=r(\cos\theta+i\sin\theta)$
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+nariši
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Fourierova vrsta
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{multicols}{2}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+https://en.wikipedia.org/wiki/Square_wave?useskin=vector#/media/File:SquareWaveFou
+rierArrows.gif
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+\begin_inset Formula $f(t)=A_{1}\cos(\omega_{1}t)+A_{2}\cos(\omega_{2}t)+...$
+\end_inset
+
+ 
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $S(x)=\frac{4}{\pi}(\sin\omega x+\frac{1}{3}\sin3\omega x+$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\ \ \ \ \ \ \ \frac{1}{5}\sin5\omega x+...)$
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+vfill
+\backslash
+null
+\backslash
+columnbreak
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename series.png
+	width 30text%
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{multicols}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Fourierova vrsta
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename wolfram.png
+	width 82text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Različna valovanja kot neskončna Fourierova vrsta
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Fourierova transformacija
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename transformacija.png
+	width 78text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Fourierova transformacija je matematični postopek, ki nam omogoča razcep
+ signalov na sestavne frekvence.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Fourierova transformacija
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Intuicija
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+https://prajwalsouza.github.io/Experiments/Fourier-Transform-Visualization.html
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+url{http://4a.si/fourier}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename trans.png
+	width 78text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Intuitivno si lahko FT predstavljamo kot navijanje amplitud po enotski krožnici.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Fourierova transformacija
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Matematična oblika
+\end_layout
+
+\begin_layout Standard
+Kako to navijanje predstavimo matematično
+\begin_inset Formula 
+\[
+\hat{f}(\nu)=\int_{-\infty}^{\infty}f(t)\cdot e^{-i2\pi\nu t}dt
+\]
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Diskretna funkcija
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+funkcija 
+\begin_inset Formula $f(x)$
+\end_inset
+
+ je zvezna, če
+\begin_inset Formula 
+\[
+\forall x_{0}\in D_{f}\text{, velja }\lim_{x\to x_{0}}f(x)=f(x_{0})\text{.}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+diskretna funkcija je funkcija, katere spremenljivka zavzema le nekatere
+ realne vrednosti.
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Vzorčeni signali
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Za praktično obdelavo zvezne signale iz narave periodično vzorčimo
+\end_layout
+
+\begin_layout Itemize
+Vzorčenje je shranjevanje amplitude signala na določen časovni interval
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Dobimo časovno diskreten signal, ki ga predstavlja niz števil
+\begin_inset Formula 
+\[
+x[n]\ \ \ n\in\mathbb{Z},\ x[n]\in I
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $n$
+\end_inset
+
+ označuje zaporedno številko vzorca
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+frekvenca vzorčenja 
+\begin_inset Formula $\nu_{vz}$
+\end_inset
+
+, interval vzorčanja 
+\begin_inset Formula $t_{vz}$
+\end_inset
+
+, kvantizacijski interval 
+\begin_inset Formula $I$
+\end_inset
+
+ (določen s številom bitov za zapis številk: 
+\begin_inset Formula $[0,2^{b}-1]$
+\end_inset
+
+)
+\end_layout
+
+\begin_layout Itemize
+Primer: mikrofon, EKG, merilnik temperature, merilnik tlaka, radijski sprejemnik
+, ...
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Vzorčeni signali
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename sampling.png
+	width 82text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Vzorčenje funkcije 
+\begin_inset Formula $S(t)$
+\end_inset
+
+ v zaporedje 
+\begin_inset Formula $S_{i}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Vzorčeni signali
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Teorija Nyquist-Shannon o vzorčenju
+\end_layout
+
+\begin_layout Itemize
+Povezava med 
+\begin_inset Formula $\nu_{max}$
+\end_inset
+
+ vzorčenega signala in 
+\begin_inset Formula $\nu_{vz}$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Za reprezentacijo signala 
+\begin_inset Formula $v_{max}$
+\end_inset
+
+ mora biti 
+\begin_inset Formula $\nu_{vz}\geq2\nu_{max}$
+\end_inset
+
+.
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename nyquistshannon.png
+	width 80text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+\begin_inset Formula $\lambda/2<t_{vz}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Diskretna Fourierova transformacija
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Ker ne gre za časovno zvezni signal, ne moremo uporabiti integracije, ampak
+ vsoto preko vseh vzorcev.
+\end_layout
+
+\begin_layout Itemize
+Namesto oblike za časovno zvezni signal
+\begin_inset Formula 
+\[
+\hat{f}(\nu)=\int_{-\infty}^{\infty}f(t)\cdot e^{-i2\pi\nu t}\ dt
+\]
+
+\end_inset
+
+za časovno diskretni signal z 
+\begin_inset Formula $N$
+\end_inset
+
+ vzorci uporabimo
+\begin_inset Formula 
+\[
+\hat{f}[\nu]=\sum_{n=0}^{N}f[n]\cdot e^{-i2\pi\nu nt_{vz}}\text{.}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+DFT je frekvenčno diskretna, vrednosti amplitud izračunamo samo za diskretne
+ frekvenčne komponente.
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Diskretna Fourierova transformacija
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Značilnost
+\end_layout
+
+\begin_layout Itemize
+Ločljivost med frekvenčnimi komponentami je pogojena z 
+\begin_inset Formula $N$
+\end_inset
+
+.
+\end_layout
+
+\end_deeper
+\begin_layout FragileFrame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Diskretna Fourierova transformacija
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Naivni algoritem v psevdokodi
+\end_layout
+
+\begin_layout Standard
+\begin_inset listings
+lstparams "language=Python,basicstyle={\ttfamily},breaklines=true"
+inline false
+status open
+
+\begin_layout Plain Layout
+
+število vzorci[] = {...}
+\end_layout
+
+\begin_layout Plain Layout
+
+število frekvence[] = {1000, 2000, 3000, 4000}
+\end_layout
+
+\begin_layout Plain Layout
+
+število težišča[frekvence_length]
+\end_layout
+
+\begin_layout Plain Layout
+
+for frekvenca in range(frekvence.length):
+\end_layout
+
+\begin_layout Plain Layout
+
+    for vzorec in range(vzorci.length):
+\end_layout
+
+\begin_layout Plain Layout
+
+        težišča[frekvenca] += vzorci[vzorec] * pow(e, -i*2*pi*frekvence[frekvenc
+a]*vzorec/vzorčna_frekvenca)
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout FragileFrame
+
+\end_layout
+
+\begin_layout FragileFrame
+
+\end_layout
+
+\begin_layout FragileFrame
+
+\end_layout
+
+\begin_layout FragileFrame
+
+\end_layout
+
+\begin_layout FragileFrame
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Diskretna Fourierova transformacija
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Časovna zahtevnost naivnega algoritma
+\end_layout
+
+\begin_layout Itemize
+Ocena časovne zahtevnosti algoritma glede na vhodne podatke: 
+\begin_inset Formula $O(...)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Naivni DFT algoritem: 
+\begin_inset Formula $O(m\cdot n)$
+\end_inset
+
+ oziroma 
+\begin_inset Formula $O(n^{2})$
+\end_inset
+
+ — polinomski čas
+\end_layout
+
+\begin_layout Itemize
+Hitra diskretna Fourierova transformacija (FFT) pa postopek optimizira na
+ 
+\begin_inset Formula $O(n\log n)$
+\end_inset
+
+.
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Obstaja več algoritmov hitre transformacije
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Gauss je 1805 že optimiziral algoritem za izračun orbit asteroidov
+\end_layout
+
+\begin_layout Itemize
+Cooley and Tukey sta 1965 predstavila moderni DIT FFT
+\end_layout
+
+\end_deeper
+\end_deeper
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Diskretna Fourierova transformacija
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Primerjava časa izvajanja
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float table
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="3">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+vzorcev
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $10000$
+\end_inset
+
+; 
+\begin_inset Formula $\SI{1}{\second}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $10\cdot10^{4}$
+\end_inset
+
+; 
+\begin_inset Formula $\SI{10}{\second}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+naiven
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $10^{8}$
+\end_inset
+
+ (1 sekunda)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $10^{10}$
+\end_inset
+
+(1,6 minute)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+FFT
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $10^{4}\cdot4$
+\end_inset
+
+ (0,0004 sekunde)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $10^{5}\cdot5$
+\end_inset
+
+ (0,0005 sekund)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="3">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+vzorcev
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $100\cdot10^{4}$
+\end_inset
+
+; 
+\begin_inset Formula $\SI{100}{\second}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $1000\cdot10^{4}$
+\end_inset
+
+; 
+\begin_inset Formula $\SI{180}{\second}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+naiven
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $10^{12}$
+\end_inset
+
+ (2,7 ure)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $10^{14}$
+\end_inset
+
+ (11 dni)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+FFT
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $10^{6}\cdot6$
+\end_inset
+
+ (0,06 sekunde)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $10^{7}\cdot7$
+\end_inset
+
+ (0,7 sekunde)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Primerjava časa izjavanja DFT in FDFT.
+ 
+\begin_inset Formula $\nu_{vz}=\SI{10000}{\per\second}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout FragileFrame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Hitra Fourierova transformacija
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Praktična uporaba v Pythonu
+\end_layout
+
+\begin_layout Itemize
+Knjižnica numpy ima vgrajen algoritem za FFT, uporaba:
+\begin_inset listings
+lstparams "language=Python,numbers=left,breaklines=true"
+inline false
+status open
+
+\begin_layout Plain Layout
+
+from numpy.fft import fft
+\end_layout
+
+\begin_layout Plain Layout
+
+import numpy as np
+\end_layout
+
+\begin_layout Plain Layout
+
+frekvencni_spekter = fft(amplituda_v_odvisnosti_od_casa)
+\end_layout
+
+\begin_layout Plain Layout
+
+print(
+\begin_inset Quotes gld
+\end_inset
+
+dominantna frekvenca: 
+\begin_inset Quotes grd
+\end_inset
+
+, np.max(frekvencni_spekter))
+\end_layout
+
+\begin_layout Plain Layout
+
+realne_vrednosti = abs(frekvencni_spekter)
+\end_layout
+
+\end_inset
+
+
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Praktična uporaba DFT/FFT
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Obdelava zvoka — izenačevalnik/equaliser
+\end_layout
+
+\begin_layout Itemize
+Kompresija slik JPEG z izgubami z dvodimenzionalnim DFT
+\end_layout
+
+\begin_layout Itemize
+Radijska komunikacija — digitalni prenos informacij preko radijskih valov
+\end_layout
+
+\begin_layout Itemize
+DTMF
+\end_layout
+
+\begin_layout Itemize
+Krovni pojem: digitalna obdelava signalov
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+DTMF — Dual tone multi frequency
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Izbiranje telefonske številke na telefonski liniji poteka preko zvoka
+\end_layout
+
+\begin_layout Itemize
+Pritiski na gumbe telefonske številčnice izdelujejo piske
+\end_layout
+
+\begin_layout Itemize
+Telefonska centrala na drugi strani s Fourierovo transformacijo piskov določi
+ pritisnjeno tipko
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename dtmf.png
+	width 72text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Pripadajoče frekvence na telefonski DTMF številčnici
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+DTMF — Dual tone multi frequency
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename dtmffreq.png
+	width 80text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Frekvenčni spekter piska, ki ga proizvaja številčnica
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Splošno načelo nedoločenosti
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Signal, zelo koncentriran v času, mora imeti široko Fourierovo transformacijo.
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Splošno načelo nedoločenosti
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Dopplerjev radar
+\end_layout
+
+\begin_layout Itemize
+Dolg signal korelira z natančno hitrostjo in široko pozicijo
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename doppler.png
+	width 80text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Dopplerjev radar
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Heisenbergovo načelo nedoločenosti
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Valovna funkcija
+\end_layout
+
+\begin_layout Itemize
+V kvantni mehaniki lahko delec opišemo s kompleksno valovno funkcijo, ki
+ je funkcija prostora in časa
+\end_layout
+
+\end_deeper
+\begin_layout Frame
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename wavelet.png
+	width 62text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Valovna funkcija
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Heisenbergovo načelo nedoločenosti
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout FrameSubtitle
+Gibalna količina prostega delca
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $p=\hbar k$
+\end_inset
+
+ (
+\begin_inset Formula $k$
+\end_inset
+
+ je prostorska frekvenca), 
+\begin_inset Formula $k=2\pi/\lambda$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Če izvedemo Fourierovo transformacijo na valovni funkciji po prostoru, dobimo
+ razporeditev amplitud po 
+\begin_inset Formula $k$
+\end_inset
+
+-ju.
+\end_layout
+
+\begin_layout Itemize
+Zaradi tega sta si nesigurnost v prostorski frekvenci in nesigurnost v poziciji
+ obratno sorazmerni
+\begin_inset Formula 
+\[
+\Delta x\cdot\Delta p=\text{konst.}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename uncertainty.png
+	width 80text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Nedoločenost pozicije in gibalne količine delca
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Konec predstavitve
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Hvala za pozornost!
+\end_layout
+
+\end_deeper
+\begin_layout Section*
+\start_of_appendix
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+All of the following is optional and typically not needed.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Section*
+\start_of_appendix
+Priloge
+\end_layout
+
+\begin_layout Subsection*
+Zahvala
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Zahvala
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+idk ...
+ šoli ig
+\end_layout
+
+\end_deeper
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection*
+\begin_inset Note Note
+status open
+
+\begin_layout Subsection*
+Literatura in dodatno branje
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 3
+status collapsed
+
+\begin_layout Plain Layout
+allowframebreaks
+\end_layout
+
+\end_inset
+
+
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Literatura in dodatno branje
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+ne navajaj vseh virov, samo najzanimivejše
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_deeper
+\begin_layout Plain Layout
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+beamertemplatebookbibitems
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+Start with overview books.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "Author1990"
+literal "true"
+
+\end_inset
+
+A.
+ Author.
+ 
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+newblock
+\end_layout
+
+\end_inset
+
+
+\emph on
+Handbook of Everything
+\emph default
+.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+newblock
+\end_layout
+
+\end_inset
+
+ Some Press, 1990.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+beamertemplatearticlebibitems
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+Followed by interesting articles.
+ Keep the list short.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "Someone2002"
+literal "true"
+
+\end_inset
+
+S.
+ Someone.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+newblock
+\end_layout
+
+\end_inset
+
+ On this and that
+\emph on
+.
+
+\emph default
+ 
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+newblock
+\end_layout
+
+\end_inset
+
+
+\emph on
+Journal on This and That
+\emph default
+.
+ 2(1):50–100, 2000.
+\end_layout
+
+\end_deeper
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Subsection*
+\begin_inset Separator plain
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+\begin_inset Argument 4
+status open
+
+\begin_layout Plain Layout
+Viri slik in dovoljenje za uporabo
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Frame
+
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Uporaba generiranega dokumenta je dovoljena v skladu s CC BY-SA (
+\begin_inset CommandInset href
+LatexCommand href
+target "http://4a.si./bysa"
+literal "true"
+
+\end_inset
+
+) 
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+Dovoljenja za uporabo LyX kode pa nisem podal!
+\end_layout
+
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+doclicenseImage[imagewidth=2cm]
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Slika 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:Shematski-prikaz-povezav"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+: Scott Martin: spremenjena, izvorna pod CC BY-SA
+\end_layout
+
+\begin_layout Itemize
+Slika 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:Drevesno-iskanje-soležnikov"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+: Limaner: izvorna pod CC BY-SA
+\end_layout
+
+\end_deeper
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/tabor/delavnica/predst/primer.py b/tabor/delavnica/predst/primer.py
new file mode 100644
index 0000000..e6f6cb3
--- /dev/null
+++ b/tabor/delavnica/predst/primer.py
@@ -0,0 +1 @@
+print("hello, world!!2")
diff --git a/tabor/delavnica/predst/sampling.png b/tabor/delavnica/predst/sampling.png
new file mode 100644
index 0000000..5414fff
--- /dev/null
+++ b/tabor/delavnica/predst/sampling.png
diff --git a/tabor/delavnica/predst/series.png b/tabor/delavnica/predst/series.png
new file mode 100644
index 0000000..dbafcd1
--- /dev/null
+++ b/tabor/delavnica/predst/series.png
diff --git a/tabor/delavnica/predst/spekter.png b/tabor/delavnica/predst/spekter.png
new file mode 100644
index 0000000..ba7305c
--- /dev/null
+++ b/tabor/delavnica/predst/spekter.png
diff --git a/tabor/delavnica/predst/square.png b/tabor/delavnica/predst/square.png
new file mode 100644
index 0000000..b1ac283
--- /dev/null
+++ b/tabor/delavnica/predst/square.png
diff --git a/tabor/delavnica/predst/tidalsum.gif b/tabor/delavnica/predst/tidalsum.gif
new file mode 100644
index 0000000..0661e87
--- /dev/null
+++ b/tabor/delavnica/predst/tidalsum.gif
diff --git a/tabor/delavnica/predst/tideforces.jpg b/tabor/delavnica/predst/tideforces.jpg
new file mode 100644
index 0000000..104fce6
--- /dev/null
+++ b/tabor/delavnica/predst/tideforces.jpg
diff --git a/tabor/delavnica/predst/trans.png b/tabor/delavnica/predst/trans.png
new file mode 100644
index 0000000..67edf8e
--- /dev/null
+++ b/tabor/delavnica/predst/trans.png
diff --git a/tabor/delavnica/predst/transformacija.png b/tabor/delavnica/predst/transformacija.png
new file mode 100644
index 0000000..5ed0603
--- /dev/null
+++ b/tabor/delavnica/predst/transformacija.png
diff --git a/tabor/delavnica/predst/uncertainty.png b/tabor/delavnica/predst/uncertainty.png
new file mode 100644
index 0000000..b265940
--- /dev/null
+++ b/tabor/delavnica/predst/uncertainty.png
diff --git a/tabor/delavnica/predst/waveform.png b/tabor/delavnica/predst/waveform.png
new file mode 100644
index 0000000..c319182
--- /dev/null
+++ b/tabor/delavnica/predst/waveform.png
diff --git a/tabor/delavnica/predst/wavelet.jpg b/tabor/delavnica/predst/wavelet.jpg
new file mode 100644
index 0000000..18e525a
--- /dev/null
+++ b/tabor/delavnica/predst/wavelet.jpg
diff --git a/tabor/delavnica/predst/wavelet.png b/tabor/delavnica/predst/wavelet.png
new file mode 100644
index 0000000..1108f89
--- /dev/null
+++ b/tabor/delavnica/predst/wavelet.png
diff --git a/tabor/delavnica/predst/wolfram.png b/tabor/delavnica/predst/wolfram.png
new file mode 100644
index 0000000..2c3b9b3
--- /dev/null
+++ b/tabor/delavnica/predst/wolfram.png
diff --git a/tabor/delavnica/py/nav.py b/tabor/delavnica/py/nav.py
new file mode 100755
index 0000000..b7468a9
--- /dev/null
+++ b/tabor/delavnica/py/nav.py
@@ -0,0 +1,20 @@
+#!/usr/bin/python3
+import matplotlib.pyplot as plt
+import numpy as np
+import seaborn as sns
+sns.set()
+
+
+f = 3.0
+t = np.arange(0,2,0.001) 
+
+cos_wave = np.cos(2*np.pi*f*t)
+# cos_wave = 2*m.cos(2*np.pi*f*t) + 5*m.cos(2*np.pi*f*2*t)
+
+plt.rcParams["figure.figsize"] = (12,4)
+plt.plot(t,cos_wave)
+plt.title("Cosine Wave with 3 Hz frequency")
+plt.ylabel("Amplitude")
+plt.xlabel('Time (in seconds)');
+
+plt.show()