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