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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{ \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. 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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 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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 \begin_inset Text \begin_layout Plain Layout vzorcev \end_layout \end_inset \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 \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 \begin_inset Text \begin_layout Plain Layout naiven \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $10^{8}$ \end_inset (1 sekunda) \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $10^{10}$ \end_inset (1,6 minute) \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout FFT \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $10^{4}\cdot4$ \end_inset (0,0004 sekunde) \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $10^{5}\cdot5$ \end_inset (0,0005 sekund) \end_layout \end_inset \end_inset \end_layout \begin_layout Plain Layout \align center \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout vzorcev \end_layout \end_inset \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 \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 \begin_inset Text \begin_layout Plain Layout naiven \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $10^{12}$ \end_inset (2,7 ure) \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $10^{14}$ \end_inset (11 dni) \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout FFT \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $10^{6}\cdot6$ \end_inset (0,06 sekunde) \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula $10^{7}\cdot7$ \end_inset (0,7 sekunde) \end_layout \end_inset \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