[VC] Start fourier transforms

README.md

@@ -66,7 +66,7 @@ If you find mistakes, please open an issue or fix them yourself and open a PR.
 - [Cheat-Sheet (EN)](./core/cd/cheat-sheet-jh/cd-cheat-sheet.pdf) Author: Janis Hutz
 
 #### Visual Computing
-- [Summary (EN)](./core/vc/summary/vc-summary.pdf) Author: Janis Hutz (NOTE: This is likely *not* to happen)
+There won't be a summary for this subject, only a Cheat-Sheet. Provided script is good.
 - [Cheat-Sheet (EN)](./core/vc/cheat-sheet-jh/vc-cheat-sheet.pdf) Author: Janis Hutz
 
 #### Human Computer Interaction

core/vc/cheat-sheet-jh/parts/00_computer-vision/03_fourier/00_intro.tex

@@ -0,0 +1,23 @@
+\shortdefinition[Sinusoid] $f(x) = A \cdot \sin(2 \pi ux + \psi)$ with $\psi$ phase shift, equiv: $A \cos(\psi) \sin(2\pi ux) + A \sin(\psi)\cos(2\pi ux)$
+
+\shortdefinition[Complex Exponential] $e^{i \theta} = \cos(\theta) + i \sin(\theta)$, complex conj. $e^{-i \theta} = \cos(\theta) - i \sin(\theta)$. For sinusoid: $\theta = 2\pi ux$.
+
+\shortdefinition[Cont. Time F. Ser] Sig as sum of sinusoids, $f(x) = \sum_{k = -\8}^{\8} c_k e^{i 2\pi kx \div T}$, with $T$ the period and $c_k$ fourier coeff.
+
+\shortdefinition[Cont. Time F. Transf] $F(u) = \sum_{\R} f(x)e^{-2\pi ux} \dx x$, $f(x) = \sum_{\R} F(u) e^{i 2\pi ux} \dx u$. $F(u)$ is \textit{typ} complex valued,
+
+\shortdefinition[Ampl. Spec] $A(u) = ||F(u)||$
+
+\shortdefinition[Phase Spec] $\phi(u) = \arg F(u) = \arctan\left( \frac{\mathfrak{I}(F(u))}{\mathfrak{R}(F(u))} \right)$
+
+\shortdefinition[DFT] used for analyzing discrete data. Applies base change to values via matrix multiplication.
+More general:
+\[
+    F(k) = \sum_{n = 0}^{N - 1} x_n e^{-i 2\pi kn \div N} \text{ for } k \in \{ 0, 1, \ldots, N - 1 \}
+\]
+
+For image:
+\[
+    F(u, v) = \sum_{x = 0}^{N - 1}\sum_{y = 0}^{M - 1} I(x, y) \cdot e^{-i2\pi\left( \frac{ux}{N} + \frac{vy}{M} \right)}
+\]
+% TODO: Formula to compute the matrix

core/vc/cheat-sheet-jh/parts/00_computer-vision/main.tex

@@ -7,4 +7,11 @@
 
 \subsection{Edge Detection}
 \input{parts/00_computer-vision/02_edge-detection.tex}
+
+\subsection{Fourier Transform}
+\input{parts/00_computer-vision/03_fourier/00_intro.tex}
+% \input{parts/00_computer-vision/03_fourier/}
+
+
+
 % \input{parts/00_computer-vision/}

core/vc/summary/vc-summary.tex

@@ -1,45 +0,0 @@
-\documentclass{article}
-
-\input{../../../helpers.tex}
-
-\usepackage{lmodern}
-\setFontType{sans}
-
-\setup{Visual Computing}
-
-\begin{document}
-\startDocument
-
-\vspace{1cm}
-\begin{center}
-    \includegraphics[width=0.5\linewidth]{~/projects/latex/assets/logo.jpg}
-\end{center}
-
-
-\vspace{2cm}
-\begin{center}
-    \begin{Large}
-        \quote{A funny quote by a professor}
-    \end{Large}
-
-    \hspace{3cm} - Prof. Dr. Professor Name, YEAR
-\end{center}
-
-\vspace{1.5cm}
-\begin{center}
-    HS2026, ETHZ
-
-    \begin{Large}
-        Summary of the Script and Lectures
-    \end{Large}
-\end{center}
-
-
-\newpage
-\printtoc{Aquamarine}
-
-
-
-
-
-\end{document}