% simple sinusoid at f (2fps) with a +shift of 1.1 to keep all values above
% zero
m = sin(2*pi*f*t)+1.1; % constant 1.1 is added so all values are positive
% part 1
% comment the line above (and assign a new value to it)
% add 1Hz 25% amplitude modulation to the input m, i.e. positive
% amplitude variation between 0.75 and 1.25
% Hint: the modulating sin or cos amplitude is 0.25, so you need to add 1.0
% observe the reconstructed signal, why is it not correct?
% what adjustment do you need to do to the signal so the dynamic range
% remains as before?
% insert your code here..
Answered Essay: % simple sinusoid at f (2fps) with a +shift of 1.1 to keep all values above
Expert Answer
documentclass[11pt]{articl}
usepackage{color}
usepackage{tikz}
%usepackage[latin1]{inputenc}
usepackage{pgfplots}
pgfplotsset{compat=1.11}
begin{document}
begin{center}
begin{tikzpicture}
begin{axis}[
width=linewidth,
trig format plots=rad,
axis lines = middle,
xlabel={$theta=wt$},
xlabel style={at={(1,0.5)},anchor=west},
enlargelimits,
ytick={empty},
extra y ticks={1,0.5,0,-0.5,-1},
extra y tick labels={$V_m$,$I_m$,0,$-I_m$,$-V_m$},
xtick={-6.28318, -4.7123889, …, 6.28318},
xticklabels={
$-2pi$, $-frac{3pi}{2}$, $-pi$, $frac{pi}{2}$, ,
$frac{pi}{2}$, $pi$, $frac{3pi}{2}$, $2pi$},
clip=false]
addplot[domain=-2*pi:2*pi,samples=200, red] {0.5*sin(x)};
addplot[domain=-2*pi:2*pi,samples=200, blue, dashed] {sin(x-2)};
draw[dotted,blue!40] (axis cs: 0,1.1) — (axis cs: 0,0);
draw[dotted,red!40] (axis cs: 1,1.1) — (axis cs: 1,0);
draw[dashed,olive,<->] (axis cs: 0,1.1) —
node[above,text=black,font=footnotesize]{$phi$} (axis cs: 1,1.1);
coordinate (P) at (axis cs:1.5*pi,{sin(25)});
node (labelV) at (axis cs:2*pi,{1+sin(2*pi)}) {Voltage $(V)$};
draw [red!50!black, thick, dashed, ->, shorten >=2pt] (labelV) — (P);
coordinate (Q) at (axis cs:-1.5*pi,{sin(30)});
node (labelI) at (axis cs:-2*pi,{1+sin(2*pi)}) {Current $(I)$};
draw [red!50!black, thick, dashed, ->, shorten >=2pt] (labelI) — (Q);
end{axis}
end{tikzpicture}
end{center}
end{document}
