file transfer commit

This commit is contained in:
Blizzard Finnegan 2021-12-16 20:26:01 -05:00
commit 06b47c6892
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function init
clc; close all;
global fig_num
fig_num = 1;
end

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**lab1.tex
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% File: lab1.tex
% Created: 12:59:32 Thu, 02 Sep 2021 EDT
% Last Change: 12:59:32 Thu, 02 Sep 2021 EDT
%
\documentclass[letterpaper]{article}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{cancel}
\usepackage{amssymb}
\usepackage{listings}
\usepackage[shortlabels]{enumitem}
\usepackage{lipsum}
\usepackage{soul}
\usepackage{geometry}
\geometry{portrait, margin=1in}
\date{09/02/2021}
\title{%
Lab 1\\
\large EEET-332-01:Signals, Systems, and Transforms Lab}
\author{Blizzard MacDougall}
\begin{document}
\maketitle
\pagenumbering{arabic}
\section{Section 1}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{section1.png}
\caption{Shockley's Equation Plot}
\label{fig:sect1}
\end{figure}
\newpage
\section{Section 2}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{section2.png}
\caption{Polynomial with Roots}
\label{fig:sect2}
\end{figure}
\end{document}

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function make_plot(x_data,y_data,graph_title,x_label,y_label,x2_data,y2_data,y2_marker)
global fig_num;
figure(fig_num);
fig_num=fig_num+1;
plot(x_data,y_data);
grid on;
xlabel(x_label); ylabel(y_label);
title(graph_title);
if nargin==8
hold on;
plot(x2_data,y2_data,y2_marker);
end
end

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init();
Vd=0:0.02:0.8;
Is=1e-12; n=1; Vt=0.026;
Id=Is*(exp(Vd/(n*Vt))-1);
make_plot(Vd,Id,"Section 1","Vd","Id")

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init();
x=[-15 -13 -11 -5 -2 -1 0 1 3 4]
p=[1 15 0 -9]
y=polyval(p,x)
r=roots(p)
make_plot(x,y,"Section 2b vector with Roots", "x", "y", r,[0 0 0], "*");

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init();
A=[1 2 3 4]
B=[2 4 6 8]
Btrans=B'
C=A.*B
Cmat=A*Btrans
Cerror=A*B

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init();
t= 0:0.1:2*pi;
w=4
y=(exp(1j*(w*t))-exp(-1j*(w*t)) )/(2j)
make_plot(t,y,"Section 4", "t", "y");

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function [m_ct,cm_ctr_win,yy]=fft_hanning_ifft(t,y,N,Mwin)
m_ctr=-N/2:N/2+1;
cm_ctr=fftshift(fft(y,N)/N);
cm=fft(y,N)/N;
make_stem(n,abs(cm_ctr),"Spectrum Amplitude","n","ab s(cm)");
win=zeros(size(N));
win(m_ctr)=hanning(2*Mwin+1)';
cm_ctr_win=cm_ctr*win;
yy=real(ifft(N*cm_ctr_win));
make_plot(t,yy,"Reconstructed Waveform","seconds","reconstructed Y");
end

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function [cm,yy]=fft_ifft(t,y,N)
m_ctr=-N/2:N/2+1;
cm_ctr=fftshift(fft(y,N)/N);
cm=fft(y,N)/N;
make_stem(n,abs(cm_ctr),"Spectrum Amplitude","n","ab s(cm)");
yy=real(ifft(N*cm_ctr));
make_plot(t,yy,"Reconstructed Waveform","seconds","reconstructed Y");
end

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% File: lab10Submission.tex
% Created: 08:06:00 Thu, 18 Nov 2021 EST
% Last Change: 08:06:00 Thu, 18 Nov 2021 EST
%
\documentclass[letterpaper]{article}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{cancel}
\usepackage{amssymb}
\usepackage{listings}
\usepackage[shortlabels]{enumitem}
\usepackage{soul}
%\usepackage[smartEllipses,hashEnumerators,hybrid]{markdown}
\usepackage{minted}
\usepackage{geometry}
\usepackage{dirtytalk}
\usepackage{lplfitch}
\geometry{portrait, margin=1in}
%\begin{minted}[linenos,bgcolor=LightGray]{[language]}
\date{11/18/2021}
\title{%
Lab 10 Submission\\
\large EEET--332--01:Signals, Systems, and Transforms}
\author{Blizzard MacDougall}
\begin{document}
\maketitle
\pagenumbering{arabic}
\section{Section 1}
\begin{enumerate}
\item Calculate $T_s$ and $\omega_s$:
\begin{equation}
T_s=0.5625s;\ \omega_s\approx11.17
\end{equation}
\item Complete the table for the $t$ array:
\begin{minted}{matlab}
[ 0.0000 0.5625 1.1250 1.6875 2.2500 2.8125 3.3750 3.9375
4.5000 5.0625 5.6250 6.1875 6.7500 7.3125 7.8750 8.4375]
\end{minted}
\item Complete the following matlab code.
\inputminted{matlab}{section1.m}
\item Using the spectrum amplitude and the data cursor, fill in the following blanks:
\begin{enumerate}
\item DC:m=0;\ $|c_m|=1.301$
\item $1^{st}$ harmonic: m=1;\ $|c_m|=1.449$
\item -$1^{st}$ harmonic: m=15;\ $|c_m|=1.449$
\item $2^{nd}$ harmonic: m=2;\ $|c_m|=1.339$
\item -$2^{nd}$ harmonic: m=14;\ $|c_m|=1.339$
\end{enumerate}
\item True / False : The DC value is the average value of the waveform. \hl{True}
\newpage
\item Repeat the previous fill-in-the-blank.
\begin{enumerate}
\item DC:m=0;\ $|c_m|=1.301$
\item $1^{st}$ harmonic: m=1;\ $|c_m|=1.449$
\item -$1^{st}$ harmonic: m=-1;\ $|c_m|=1.449$
\item $2^{nd}$ harmonic: m=2;\ $|c_m|=1.339$
\item -$2^{nd}$ harmonic: m=-2;\ $|c_m|=1.339$
\end{enumerate}
\item Repeat the same fill in the blank, using $\omega$ instead of $m$.
\begin{enumerate}
\item DC:$\omega=0;\ |c_m|=1.301$
\item $1^{st}$ harmonic: $\omega=0.698132;\ |c_m|=1.449$
\item -$1^{st}$ harmonic: $\omega=-0.698132;\ |c_m|=1.449$
\item $2^{nd}$ harmonic: $\omega=1.39626;\ |c_m|=1.339$
\item -$2^{nd}$ harmonic: $\omega=-1.39626;\ |c_m|=1.339$
\end{enumerate}
\end{enumerate}
\section{Section 5}
\begin{equation}
\begin{split}
T_s=0.0029297\\
f_0=\frac13\\
f_N=56.\overline8
\end{split}
\end{equation}
This system's Nyquist frequency is much greater than the frequency of either of the input sine waves. \hl{True}
\begin{enumerate}
\item What is the frequency of the $24^{th}$ harmonic?
\begin{equation}
24(f_0)=24*\frac13=8Hz
\end{equation}
\item What is m equal to at each of the spikes in the spectrum?
\begin{minted}{matlab}
[ -45 -24 0 24 45 ]
\end{minted}
\item Convert these sample numbers to frequency.
\begin{minted}{matlab}
[ -15Hz 8Hz DC 8Hz 15Hz ]
\end{minted}
\end{enumerate}
\end{document}

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T=5;
t=0:T/5:T;
y1=zeros(size(t));
y2=zeros(size(t));
t_greater_than_2=find(t>2);
y2(t_greater_than_2)=3*t(t_greater_than_2);
y3=zeros(size(t));
t_between_1_and_3=find(t>=1&t<=3);
y3(t_between_1_and_3)=3;

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init();
N=16;
n=0:N-1;
T=9;
Ts=T/N;
t=0:Ts:T-Ts;
y=zeros(size(t));
t_between_1_and_2=find(t>=1&t<=2);
y(t_between_1_and_2)=-t(t_between_1_and_2);
t_between_7_and_9=find(t>7&t<=9);
y(t_between_7_and_9)=7t(t_between_7_and_9);
make_plot(t,y,'Input Function','n','y');
fft_ifft(t,n,y,N);

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init();
N=1024;
n=0:N-1;
T=9;
Ts=T/N;
t=0:Ts:T-Ts;
y=zeros(size(t));
t_between_1_and_2=find(t>=1&t<=2);
y(t_between_1_and_2)=-t(t_between_1_and_2);
t_between_7_and_8=find(t>7&t<=8);
y(t_between_7_and_8)=sin(((2*pi)/(T*p))*t(t_between_7_and_8));
make_plot(t,y,'Input Function','n','y');
fft_ifft(t,n,y,N);

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init();
N=16;
M=3;
m=-N/2:N/2-1;
cm=2*abs(m);
make_stem(m,cm,'Spectrum','m','cm');
win=zeros(size(m));
m_between_negM_and_posM=find(m>-M&m<M);
win(m_between_negM_and_posM)=hanning(2*M+1);
make_stem(m,win,'Window','m','win');
cm_win=cm.*win;
make_stem(m,cm_win,'Windowed Spectrum','m','cm_win');

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init();
N=1024;
n=0:N-1;
T=9;
Ts=T/N;
t=0:Ts:T-Ts;
y=zeros(size(t));
t_between_1_and_2=find(t>=1&t<=2);
y(t_between_1_and_2)=sin(((2*pi)/(T*p))*t(t_between_1_and_2);
t_between_7_and_8=find(t>7&t<=8);
y(t_between_7_and_8)=sin(((2*pi)/(T*p))*t(t_between_7_and_8));
make_plot(t,y,'Input Function','n','y');
Mwin=128;
[m_ctr,cm_ctr,yy]=fft_hanning_ifft(t,n,y,N);

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init();
N=1024;
n=0:N-1;
T=9;
Ts=T/N;
A=10;
Tsine=1/2;
t=0:Ts:T-Ts;
y=zeros(size(t));
t_between_1_and_2=find(t>=1&t<=2);
y(t_between_1_and_2)=A*sin(((2*pi)/(Tsine))t(t_between_1_and_2));
t_between_3_and_5=find(t>3&t<=5);
y(t_between_7_and_8)=2*t(t_between_7_and_8)+6;
make_plot(t,y,'Input Function','n','y');
Mwin=128;
[m_ctr,cm_ctr,yy]=fft_hanning_ifft(t,n,y,N);

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init();
N=1024;
n=0:N-1;
T=9;
Ts=T/N;
A=10;
Tsine=1/2;
t=0:Ts:T-Ts;
w1=8*2*pi;
w2=15*2*pi;
y=10+5*sin(w1*t)+16*sin(w2*t);
make_plot(t,y,'Input Function','n','y');
Mwin=128;
[m_ctr,cm_ctr,yy]=fft_hanning_ifft(t,n,y,N);

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function init
clc; close all;
global fig_num
fig_num = 1;
end

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% File: lab2.tex
% Created: 07:55:46 Thu, 09 Sep 2021 EDT
% Last Change: 07:55:46 Thu, 09 Sep 2021 EDT
%
\documentclass[letterpaper]{article}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{cancel}
\usepackage{amssymb}
\usepackage{listings}
\usepackage[shortlabels]{enumitem}
\usepackage{lipsum}
\usepackage{soul}
\usepackage{geometry}
\geometry{portrait, margin=1in}
\date{09/09/2021}
\title{%
Lab 2\\
\large EEET-332-01:Signals, Systems, and Transforms}
\author{Blizzard MacDougall}
\begin{document}
\maketitle
\pagenumbering{arabic}
\section{Section 1}
\begin{lstlisting}[language=matlab]
init()
t=linspace(0, 4*pi, 201)
w=0.5
phase=-pi/3
theta=w*t+phase;
y=(exp(1j*theta)+exp(-1j*theta))/2;
make_plot(t,y,"Section 1: Cosine Wave with 60 degree shift","Time (t)","Amplitude (y)")
\end{lstlisting}
\section{Section 2}
\begin{lstlisting}[language=matlab]
init()
x=linspace(0,10,1751)
num=[1 0 -16];
ynum=polyval(num,x)
den=[1 -4]
yden=polyval(den,x)
y=ynum./yden
k=find(isnan(y))
x(k)
y(k)=4
make_plot(x,y,"Section 2: (x^2-16)/(x-4)","x","y")
\end{lstlisting}
\section{Section 3}
\begin{lstlisting}[language=matlab]
init()
t=linspace(0,20,201);
ey=exp(-0.2.*t)
y=ey.*cos(t)
make_plot(t,y,"Section 3: Damping Equation")
\end{lstlisting}
\newpage
\section{Section 4}
Identify the Euler Phasor and complex $s$ variable.
\begin{enumerate}[a)]
\item $x(t)=4\cos(5t+60)$\\
$\overrightarrow X=4\angle60^\circ$\\
$s=j5$
\item $x(t)=3\cos(2t+12)$\\
$\overrightarrow X=3\angle12^\circ$\\
$s=j2$\\
\item $x(t)=\cos(t)$\\
$\overrightarrow X=1\angle0^\circ$\\
$s=j$
\end{enumerate}
\end{document}

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function make_plot(x_data,y_data,graph_title,x_label,y_label,x2_data,y2_data,y2_marker)
global fig_num;
figure(fig_num);
fig_num=fig_num+1;
plot(x_data,y_data);
grid on;
xlabel(x_label); ylabel(y_label);
title(graph_title);
if nargin==8
hold on;
plot(x2_data,y2_data,y2_marker);
end
end

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init()
t=linspace(0, 4*pi, 201)
w=0.5
phase=-pi/3
theta=w*t+phase;
y=(exp(1j*theta)+exp(-1j*theta))/2;
make_plot(t,y,"Section 1: Cosine Wave with 60 degree shift","Time (t)","Amplitude (y)")

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init()
x=linspace(0,10,1751)
num=[1 0 -16];
ynum=polyval(num,x)
den=[1 -4]
yden=polyval(den,x)
y=ynum./yden
k=find(isnan(y))
x(k)
y(k)=8
make_plot(x,y,"Section 2: (x^2-16)/(x-4)","x","y")

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init()
t=linspace(0,20,201);
ey=exp(-0.2.*t)
y=ey.*cos(t)
make_plot(t,y,"Section 3: Damping Equation","x","y")

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function [mag_y, theta_y]=forced_resp_solver (num,den,mag_x,theta_x,sigma,omega)
s=sigma+(1j*omega);
x=mag_x*exp(1j*theta_x);
Y=(polyval(num,s)./polyval(den,s)).*x;
mag_y=abs(Y); theta_y=angle(Y);
disp(['Output vector Y= ' num2str(mag_y) 'e^(' num2str(theta_y) 'j)']);
end

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function init
clc; close all;
global fig_num
fig_num = 1;
end

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% File: lab3Report.tex
% Created: 23:02:38 Thu, 23 Sep 2021 EDT
% Last Change: 23:02:38 Thu, 23 Sep 2021 EDT
%
\documentclass[letterpaper]{article}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{cancel}
\usepackage{amssymb}
\usepackage{listings}
\usepackage[shortlabels]{enumitem}
\usepackage{lipsum}
\usepackage{soul}
\usepackage{geometry}
\geometry{portrait, margin=1in}
\date{09/23/2021}
\title{%
Lab 3 Report\\
\large EEET-332-01:Signals, Systems, and Transforms Lab}
\author{Blizzard MacDougall}
\begin{document}
\maketitle
\pagenumbering{arabic}
\section{Section 1}
\begin{figure}[h!]
\includegraphics{section1.png}
\end{figure}
\newpage
\section{Section 4}
\begin{enumerate}[a)]
\item $x=2$
\begin{equation}
\begin{split}
\overrightarrow X=2\angle0^\circ\\
s=0\\
\overrightarrow Y=1
\end{split}
\end{equation}
\item $x=6\cos(3t+30^\circ)$
\begin{equation}
\begin{split}
\overrightarrow X=6\angle30^\circ=6e^{0.52359878j}\\
s=3j\\
\overrightarrow Y=0.98361e^{1.1671j}
\end{split}
\end{equation}
\end{enumerate}
Final Equation:$y(t)=1+0.98361*\cos(3t+66.86990427)$
\end{document}

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function make_plot(x_data,y_data,graph_title,x_label,y_label,x2_data,y2_data,y2_marker)
global fig_num;
figure(fig_num);
fig_num=fig_num+1;
plot(x_data,y_data);
grid on;
xlabel(x_label); ylabel(y_label);
title(graph_title);
if nargin==8
hold on;
plot(x2_data,y2_data,y2_marker);
end
end

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function natural_resp_solver(den);
disp("Poles for the natural response");
poles=roots(den)
end

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Section 1
Output vector Y= 0.10523e^(-2.7539j)
Section 2
poles =
-0.5000 + 0.5000i
-0.5000 - 0.5000i
Section 3
N/A
Section 4
a
X=2<0
s=0
Y=1
b
X=6<30
S=3j
Y= 0.98361e^(1.1671j)
y(t)=1+0.98361*cos(3t+66.86990427)

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init();
disp('Section 1 Example 1');
sigma = 0; omega = 10;
mag_x= 2; theta_x= 5*(pi/180);
t=linspace(0,0.5,1000);
x_t=mag_x*cos(omega*t+theta_x);
make_plot(t,x_t,'Section 1 Input','t','x');
num=[5 0]; den=[1 4 4 8];
[mag_y, theta_y]=forced_resp_solver(num,den,mag_x,theta_x,sigma,omega)
y_t=mag_y*cos(omega*t+theta_y);
make_plot(t,y_t,'Section 1 Response','t','y');

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init();
disp('Section 1 Example 1');
sigma = 0; omega = 10;
mag_x= 2; theta_x= 5*(pi/180);
t=linspace(0,5,1000);
x_t=mag_x*cos(omega*t+theta_x);
make_plot(t,x_t,'Section 1 Input','t','x');
num=[5 0]; den=[1 4 4 8];
[mag_y, theta_y]=forced_resp_solver(num,den,mag_x,theta_x,sigma,omega)
y_t=mag_y*cos(omega*t+theta_y);
make_plot(t,y_t,'Section 1 Response','t','y');

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init();
disp('Section 1 Example 1');
sigma = 0; omega = 100;
mag_x= 4; theta_x= 30*(pi/180);
t=linspace(0,0.5,1000);
x_t=mag_x*cos(omega*t+theta_x);
make_plot(t,x_t,'Section 2 Input','t','x');
num=[1]; den=[2 2 1];
natural_resp_solver(den);
[mag_y, theta_y]=forced_resp_solver(num,den,mag_x,theta_x,sigma,omega)
y_t=mag_y*cos(omega*t+theta_y);
make_plot(t,y_t,'Section 2 Response','t','y');

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init();
t=linspace(0,25,1000);
num=[1];
den=[2 -2 1];
yi= impulse(tf(num,den),t);
make_plot(t,yi,"Section 3: Impulse Response","t","y")
%pzmap(tf(num,den));

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init();
disp('Section 4 Example 1');
sigma = 0; omega = 0;
mag_x= 2; theta_x= %30*(pi/180);
t=linspace(0,0.5,1000);
x_t=mag_x*cos(omega*t+theta_x);
make_plot(t,x_t,'Section 4 Input','t','x');
num=[1 -2 1]; den=[1 2 16 18 2];
natural_resp_solver(den);
[mag_y, theta_y]=forced_resp_solver(num,den,mag_x,theta_x,sigma,omega)
y_t=mag_y*cos(omega*t+theta_y);
make_plot(t,y_t,'Section 4 Response','t','y');

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init();
disp('Section 4 Example 1');
sigma = 0; omega = 3;
mag_x= 6; theta_x= 30*(pi/180);
t=linspace(0,0.5,1000);
x_t=mag_x*cos(omega*t+theta_x);
make_plot(t,x_t,'Section 4 Input','t','x');
num=[1 -2 1]; den=[1 2 16 18 2];
natural_resp_solver(den);
[mag_y, theta_y]=forced_resp_solver(num,den,mag_x,theta_x,sigma,omega)
y_t=mag_y*cos(omega*t+theta_y);
make_plot(t,y_t,'Section 4 Response','t','y');

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function [mag_y, theta_y]=forced_resp_solver (num,den,mag_x,theta_x,sigma,omega)
s=sigma+(1j*omega);
x=mag_x*exp(1j*theta_x);
Y=(polyval(num,s)./polyval(den,s)).*x;
mag_y=abs(Y); theta_y=angle(Y);
disp(['Output vector Y= ' num2str(mag_y) 'e^(' num2str(theta_y) 'j)']);
end

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function init
clc; close all;
global fig_num
fig_num = 1;
end

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function make_plot(x_data,y_data,graph_title,x_label,y_label,x2_data,y2_data,y2_marker)
global fig_num;
figure(fig_num);
fig_num=fig_num+1;
plot(x_data,y_data);
grid on;
xlabel(x_label); ylabel(y_label);
title(graph_title);
if nargin==8
hold on;
plot(x2_data,y2_data,y2_marker);
end
end

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function natural_resp_solver(den);
disp("Poles for the natural response");
poles=roots(den)
end

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disp('Section 1: Finding Transfer Function');
syms s R L C Zc Zp TF
eqn1 = Zp==R*s*L/(R+s*L);
Zp = solve(eqn1,Zp)
eqn2 = Zc==1/(s*C);
Zc = solve(eqn2,Zc)
eqn3 = TF==Zp/(Zc+Zp);
TF = solve(eqn3,TF)
R=2; L=5; C=2;
TF = subs(TF)

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init();
disp('Section 1: Finding Transfer Function');
syms s R L C Zc Zp TF
eqn1 = Zp==R*s*L/(R+s*L);
Zp = solve(eqn1,Zp)
eqn2 = Zc==1/(s*C);
Zc = solve(eqn2,Zc)
eqn3 = TF==Zp/(Zc+Zp);
TF = solve(eqn3,TF)
R=2; L=5; C=2;
TF = subs(TF)
[symNum,symDen]=numden(TF)
num=sym2poly(symNum)
den=sym2poly(symDen)
polyTF=tf(num,den)
[yi,t]=impulse(polyTF);
roots(den)
make_plot(t,yi,'Section 2 Impulse Response','t','yi');

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init();
disp('Section 3: Finding Transfer Function');
syms s R L C Zc Zp TF
eqn1 = Zp==R+L*s;
Zp = solve(eqn1,Zp)
eqn2 = Zc==1/(s*C);
Zc = solve(eqn2,Zc)
eqn3 = TF==Zc/(Zc+Zp);
TF = solve(eqn3,TF)

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init();
disp('Section 1: Finding Transfer Function');
syms s R L C Zc Zp TF
eqn1 = Zp==R+L*s;
Zp = solve(eqn1,Zp)
eqn2 = Zc==1/(s*C);
Zc = solve(eqn2,Zc)
eqn3 = TF==Zc/(Zc+Zp);
TF = solve(eqn3,TF)
R=1; L=1; C=1;
TF = subs(TF)
[symNum,symDen]=numden(TF)
num=sym2poly(symNum)
den=sym2poly(symDen)
polyTF=tf(num,den)
[yi,t]=impulse(polyTF);
roots(den)
make_plot(t,yi,'Section 4 Impulse Response','t','yi');

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init();
disp('Section 1: Finding Transfer Function');
syms s R L C Zc Zp TF
eqn1 = Zp==R+L*s;
Zp = solve(eqn1,Zp)
eqn2 = Zc==1/(s*C);
Zc = solve(eqn2,Zc)
eqn3 = TF==Zc/(Zc+Zp);
TF = solve(eqn3,TF)
R=2; L=1; C=1;
TF = subs(TF)
[symNum,symDen]=numden(TF)
num=sym2poly(symNum)
den=sym2poly(symDen)
polyTF=tf(num,den)
[yi,t]=impulse(polyTF);
roots(den)
make_plot(t,yi,'Section 4 Impulse Response','t','yi');

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init();
disp('Section 1: Finding Transfer Function');
syms s R L C Zc Zp TF
eqn1 = Zp==R+L*s;
Zp = solve(eqn1,Zp)
eqn2 = Zc==1/(s*C);
Zc = solve(eqn2,Zc)
eqn3 = TF==Zc/(Zc+Zp);
TF = solve(eqn3,TF)
R=4; L=1; C=1;
TF = subs(TF)
[symNum,symDen]=numden(TF)
num=sym2poly(symNum)
den=sym2poly(symDen)
polyTF=tf(num,den)
[yi,t]=impulse(polyTF);
roots(den)
make_plot(t,yi,'Section 4 Impulse Response','t','yi');

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\relax
\@writefile{toc}{\contentsline {section}{\numberline {1}Section 1}{1}{}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {2}Section 2}{1}{}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Impulse Response}}{1}{}\protected@file@percent }
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% File: submissionDoc.tex
% Created: 18:54:03 Wed, 13 Oct 2021 EDT
% Last Change: 18:54:03 Wed, 13 Oct 2021 EDT
%
\documentclass[letterpaper]{article}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{cancel}
\usepackage{amssymb}
\usepackage{listings}
\usepackage[shortlabels]{enumitem}
\usepackage{lipsum}
\usepackage{soul}
\usepackage{geometry}
\geometry{portrait, margin=1in}
\date{10/13/2021}
\title{%
Lab 4\\
\large EEET-332-01: Signals, Systems, and Transforms Lab}
\author{Blizzard MacDougall}
\begin{document}
\maketitle
\pagenumbering{arabic}
\section{Section 1}
\begin{equation}
\begin{split}
Z_p=\frac{RLs}{R+Ls}=\frac{10s}{2+5s}\\
Z_t=\frac{R+Ls+RLCs^2}{Cs(R+Ls)}=\frac{20s^2+5s+2}{2s(5s+2)}\\
\frac{V_o}{V_i}=\frac{Z_p}{Z_t}=\frac{\frac{RLs}{R+Ls}}{\frac{R+Ls+RLCs^2}{Cs(R+Ls)}}=\frac{RLs}{\cancel{R+Ls}}\times\frac{Cs\cancel{(R+Ls)}}{RLCs^2+Ls+R}\\
\frac{V_o}{V_i}=\frac{RLCs^2}{RLCs^2+Ls+R}=\frac{20s^2}{20s^2+5s+2}
\end{split}
\end{equation}
\section{Section 2}
\begin{figure}[h!]
\centering
\includegraphics[height=8cm]{section2.png}
\caption{Impulse Response}
\end{figure}
Roots: $-0.125\pm0.2905i$
All roots are positive.
\end{document}

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function [mag_y, theta_y]=forced_resp_solver (num,den,mag_x,theta_x,sigma,omega)
s=sigma+(1j*omega);
x=mag_x*exp(1j*theta_x);
Y=(polyval(num,s)./polyval(den,s)).*x;
mag_y=abs(Y); theta_y=angle(Y);
disp(['Output vector Y= ' num2str(mag_y) 'e^(' num2str(theta_y) 'j)']);
end

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function init
clc; close all;
global fig_num
fig_num = 1;
end

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function init_bode
clc; close all;
global s
s=tf('s');
global fig_num
fig_num=1;
global options
options = bodeoptions;
end

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function make_bode (mag_plot, phase_plot, H, log_xmin, log_xmax, ymin, ymax)
global fig_num;
figure(fig_num);
fig_num = fig_num + 1;
global options;
options.Ylim = [ymin ymax];
options.MagVisible = mag_plot;
options.PhaseVisible = phase_plot;
w=logspace(log_xmin,log_xmax,1000);
bode(H,options,w); grid on;
end

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function make_plot(x_data,y_data,graph_title,x_label,y_label,x2_data,y2_data,y2_marker)
global fig_num;
figure(fig_num);
fig_num=fig_num+1;
plot(x_data,y_data);
grid on;
xlabel(x_label); ylabel(y_label);
title(graph_title);
if nargin==8
hold on;
plot(x2_data,y2_data,y2_marker);
end
end

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function natural_resp_solver(den);
disp("Poles for the natural response");
poles=roots(den)
end

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init_bode{};
global s
H=4*(s+0.5)/s;
minreal(H)
make_bode('on','off',H,-2,1,0,60);
make_bode('off','on',H,-2,1,-90,0);

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init_bode{};
global s
H=12*(s+1.5)/(s*(s+3));
minreal(H)
make_bode('on','off',H,-2,1,0,60);
make_bode('off','on',H,-2,1,-90,0);

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init_bode{};
global s
H=2*(s-2)/((s+2)^2);
minreal(H)
make_bode('on','off',H,-2,1,0,60);
make_bode('off','on',H,-2,1,-90,0);

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init_bode();
global s
p =(s);
H=((1.414)/(p^2+0.6265*p+1.1424))*((0.6265)/(p+0.6265));
minreal(H)
make_bode('on','off',H,2,6,-40,5);
make_bode('off','on',H,2,6,-180,0);

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init_bode();
global s
p = (s)/(2*pi()*10000);
H=((1.1424)/((p^2)+(0.6265*p)+1.1424))*((0.6265)/(p+0.6265));
minreal(H)
make_bode('on','off',H,2,6,-40,5);
make_bode('off','on',H,2,6,-180,0);

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