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midterm.tex

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+\documentclass{article}
+\usepackage[utf8x]{inputenc}
+\usepackage[margin=1in]{geometry} % Adjust margins
+\usepackage{caption}
+\usepackage{wrapfig}
+\usepackage{subcaption}
+\usepackage{parskip} % dont indent after paragraphs, figures
+\usepackage{xcolor}
+%\usepackage{csquotes} % Recommended for biblatex
+\usepackage{tikz}
+\usepackage{pgfplots}
+\usetikzlibrary{positioning}
+\usepackage{float}
+\usepackage{amsmath}
+\PassOptionsToPackage{hyphens}{url}
+\usepackage{hyperref} % allows urls to follow line breaks of text
+\usepackage{glossaries}
+\usepackage[style=ieee, backend=biber, maxnames=1, minnames=1]{biblatex}
+
+
+
+
+
+\title{Analog Signal Processing \\ Midterms}
+
+\begin{document}
+\maketitle
+
+\section{1. Midterm}
+\begin{enumerate}
+    \item Find $F(x)$ given  \[ f(x) =
+        \begin{cases}
+            t-1 &, (1;2) \\
+            t &, [2;4] \\
+            -\frac{1}{2} (t-6) &, (4;6] \\
+        \end{cases}
+        \]
+    \item Define the imaginary part of the system given the real part is $ H_{Re} = 4-\omega^2 \quad ,\omega \in [-2;2]$
+    \item Define the step response of a 2nd order Filter with Bessel approximation and $3.4$ kHz cutoff frequency.
+        Determine the filter parameters.
+    \item Define the transfer function of a 4th-order band-pass Chebyshev filter with central frequency $100$ MHz, $0.2$ dB passband ripple
+        and bandwidth $5$ Mhz.
+\end{enumerate}
+\section{2. Midterm}
+\begin{enumerate}
+    \item Determine the component values and draw the implementation of a passive second-order high-pass filter in an RC configuration,
+        with the component values indicated, a cutoff frequency of $250$ Hz and a Q factor of $0.35$. Choose decade values for the capacitances.
+    \item Implement, using operational amplifiers, a fourth-order low-pass filter with the normalized transfer function
+        \[H(s) = \frac{1}{s^2 + 1.8478 \cdot s + 1} \cdot \frac{1}{s^2 + 0.7654 \cdot s + 1}\]
+        Perform element denormalization for a cutoff frequency of $12$ kHz. Choose decade values for the capacitances.
+        Draw the implementatiopn with the denormalized component values.
+    \item Implement, using transconductance amplifiers ($T= 40$\textdegree C, $U_{\text{NAP}} = \pm3.3V, U_\text{D} = 0.6$V)
+        a second-order band-pass filter with a center frequency of $1$ kHz, a pole quality factor of $0.3$ and a gain of $6$ dB.
+    \item A sporting event is being covered by a drone that produces an unwanted sound at a frequency of 366 Hz.
+        Desing the simplest filter implementation that can remove this sound from the live broadcast, with a bandwidth of $\pm 5 $ Hz.
+        Determine the transfer function and sketch the amplitude-frequency characteristic in detail.
+        In the filter implementation, use all three types of passive elements, with the reactive elements connected in parallel,
+        and the filter having no power supply.
+\end{enumerate}
+\end{document}