Week 1

MATLAB/Week_1.m

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+Fs = 8000; % Sampling rate
+T = 0.2;   % Duration
+
+Fm = 10;   % Message signal frequency
+Ac = 1;    % Carrier amplitude
+Fc = 300;  % Carrier frequency
+
+samples = Fs * T;
+
+% Time vector
+t = linspace(0, T, samples + 1); t(end) = [];
+% Frequency vector
+f = linspace(-Fs / 2, Fs / 2, samples + 1); f(end) = [];
+
+x = cos(2 * pi * Fm * t);      % Message signal
+c = Ac * cos(2 * pi * Fc * t); % Carrier waveform
+
+%% DSB-SC modulation
+y1 = x .* c;
+
+figure(), title('DSB-SC'), subplot(2, 1, 1)
+plot(t, x, 'm', 'LineWidth', 1), hold on
+plot(t, c, 'c--'), plot(t, y1, 'k--')
+xlabel('Time (sec)'), ylabel('Amplitude')
+legend('m(t)', 'c(t)', 's(t)')
+
+% Spectral Characteristics of the DSB-SC signal
+X = fft(x); C = fft(c); Y = fft(y1);
+
+subplot(2, 1, 2)
+stem(f, abs(fftshift(X)) / Fs, '.m', 'LineWidth', 1), hold on
+stem(f, abs(fftshift(C)) / Fs, '.c')
+stem(f, abs(fftshift(Y)) / Fs, '.k')
+xlabel('Frequency (Hz)'), ylabel('Magnitude')
+legend('M(f)', 'C(f)', 'Y(f)'), axis([-2 * Fc 2 * Fc 0 0.15])
+
+%% DSB-FC modulation
+mu = 2; % Modulating index
+y2 = (1 + mu * x) .* c; 
+
+figure(), title('DSB-FC'), subplot(2, 1, 1)
+plot(t, x, 'm', 'LineWidth', 1), hold on
+plot(t, c, 'c--'), plot(t, y2, 'k--')
+xlabel('Time (sec)'), ylabel('Amplitude')
+legend('m(t)', 'c(t)', 'y(t)')
+
+% Task - Change the modulation index, and observe the resultant modulated signal.
+%        Comment on the results
+
+% Spectral Characteristics of the DSB-FC signal
+Y = fft(y2);
+
+subplot(2, 1, 2)
+stem(f, abs(fftshift(X)) / Fs, '.m', 'LineWidth', 1), hold on
+stem(f, abs(fftshift(C)) / Fs, '.c')
+stem(f, abs(fftshift(Y)) / Fs, '.k')
+xlabel('Frequency (Hz)'), ylabel('Magnitude')
+legend('M(f)', 'C(f)', 'Y(f)'), axis([-2 * Fc 2 * Fc 0 0.15])
+
+%% Recovering the original signal
+x_baseband = y2;
+x_baseband(x_baseband < 0) = 0; % Rectified Signal
+
+X_filt = fft(x_baseband);               % Spectral components
+X_filt(abs(ifftshift(f)) > 2 * Fm) = 0; % Filtering to remove high frequency carrier
+
+x_demod = real(ifft(X_filt));      % Recover the signal
+x_demod = x_demod - mean(x_demod); % Remove the DC bias
+
+% Plot against original
+figure()
+hold on
+plot(t, x, 'k')
+plot(t, x_demod, 'r--')
+xlabel('Time [s]'), ylabel('Amplitude')
+legend('x(t)', 'x_{rx}(t)')

make_figures.bat

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+@ECHO OFF
+
+setlocal ENABLEDELAYEDEXPANSION
+
+@REM Display help text
+IF "%~1"=="-h" GOTO :help
+IF "%~1"=="-help" GOTO :help
+
+@REM Set global variables
+@REM Script name
+SET scriptname=%~nx0
+
+@REM Script mode
+SET /A file=0
+SET /A recursive=0
+
+@REM Options
+SET /A verbose=0
+SET /A open=0
+
+SET /A tex="a"
+
+@REM Set mode
+IF "%1"=="" GOTO :noMode
+
+IF "%1"=="recursive" (
+    SET recursive=1
+) ELSE (
+    IF "%1"=="file" (
+        SET file=1
+    ) ELSE (
+        GOTO :invalidMode
+    )
+)
+
+SHIFT
+SET directory=%~1
+SHIFT
+
+IF %file%==1 (
+    SET tex=%~1
+    SHIFT
+)
+
+@REM If no parameters, build without opening
+IF "%1"=="" GOTO :default
+
+@REM Loop through all parameters
+SET /A numP=0
+
+:loop
+    @REM Use numP to test each parameter for validity
+    SET numP=0
+
+    @REM Check options
+    IF "%1"=="-v" (
+        SET numP=1
+        SET verbose=1
+    ) ELSE (
+        IF "%1"=="-verbose" (
+            SET numP=1
+            SET verbose=1
+        )
+    )
+    IF "%1"=="-o" (
+        SET numP=1
+        SET open=1
+    ) ELSE (
+        IF "%1"=="-open" (
+            SET numP=1
+            SET open=1
+        )
+    )
+
+    @REM If current option is not valid
+    IF !numP!==0 GOTO :invalidOption
+
+    @REM Shift variables and loop if another option exists
+    SHIFT
+    IF NOT "%1"=="" GOTO :loop
+
+:: Default
+:default
+    IF NOT EXIST "%directory%" GOTO :invalidDirectory
+
+    IF %recursive%==1 (
+        FOR /R "%directory%" %%i IN (*.TIKZ) DO (
+            SET tex=%%~ni
+            CALL :main
+        )
+    ) ELSE (
+        CALL :main
+    )
+
+    @REM Finally:
+    GOTO :EOF
+
+:: Main function
+:main
+    @REM Verbose options
+    IF %verbose%==0 (
+        CALL :buildPDF
+    ) ELSE (
+        CALL :buildPDFv
+    )
+
+    @REM Open options
+    IF %open%==1 (
+        CALL :openPDF
+    )
+
+    EXIT /B
+
+:: Build PDF
+:buildPDF
+    ECHO -- Building PDF --
+    latexmk -aux-directory=Debug -shell-escape -file-line-error -interaction=nonstopmode -halt-on-error -output-directory=figures -silent -xelatex %directory%/%tex%.tikz
+    EXIT /B
+
+:: Build PDF verbose
+:buildPDFv
+    ECHO -- Building PDF -- (v)
+    latexmk -aux-directory=Debug -shell-escape -file-line-error -interaction=nonstopmode -halt-on-error -output-directory=figures -verbose -xelatex %directory%/%tex%.tikz
+    EXIT /B
+
+:: Open PDF
+:openPDF
+    ECHO -- Opening PDF --
+    figures\%tex%.pdf
+    EXIT /B
+
+:: Help
+:help
+    ECHO %scriptname% compile tikz diagrams using XeLaTeX.
+    ECHO.
+    ECHO     Usage: %scriptname% file [directory] [filename] [options]
+    ECHO            %scriptname% recursive [directory] [options]
+    ECHO.
+    ECHO Available options:
+    ECHO     %scriptname% [-h ^| -help]                  Provides help information.
+    ECHO     %scriptname% [filename] [-v ^| -verbose]    Show compiler output.
+    ECHO     %scriptname% [filename] [-o ^| -open]       Open the PDF after compilation.
+    GOTO :EOF
+
+:: No Mode
+:noMode
+    ECHO No mode provided. [file ^| recursive] expected.
+    ECHO Try "%scriptname% -h" for more information.
+    GOTO :EOF
+
+:: Invalid Option
+:invalidOption
+    ECHO Unknown option: %1
+    ECHO Try "%scriptname% -h" for more information.
+    GOTO :EOF
+
+:: Invalid Mode
+:invalidMode
+    ECHO Invalid mode provided. [file ^| recursive] expected.
+    ECHO Try "%scriptname% -h" for more information.
+    GOTO :EOF
+
+:: No Directory
+:noDirectory
+    ECHO No directory was supplied.
+    ECHO Try "%scriptname% -h" for more information.
+    GOTO :EOF
+
+:: Invalid Directory
+:invalidDirectory
+    ECHO Directory "%directory%" is invalid.
+    ECHO Try "%scriptname% -h" for more information.
+    GOTO :EOF

tikz/communications_system.tikz

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+%!TEX TS-program = xelatex
+%!TEX options = -aux-directory=Debug -shell-escape -file-line-error -interaction=nonstopmode -halt-on-error -synctex=1 "%DOC%"
+\documentclass{standalone}
+
+\usepackage{unicode-math}
+\setmathfont{Latin Modern Math}
+\setmathfont{TeX Gyre Pagella Math}[range={bb,bbit}, Scale=MatchUppercase]
+
+\usepackage[dvipsnames]{xcolor}
+\usepackage{tikz}
+\usetikzlibrary{positioning,decorations.pathreplacing,calligraphy}
+
+\begin{document}
+\begin{tikzpicture}
+    \node [
+        draw,
+        fill=SeaGreen,
+        text width=2cm,
+        inner sep=0.3cm,
+        align=center,
+        minimum height=1.2cm
+    ] (sp1) {Signal\\ Processing};
+    \node [
+        draw,
+        fill=SeaGreen,
+        text width=2cm,
+        minimum height=1.2cm,
+        inner sep=0.3cm,
+        align=center,
+        right=1cm of sp1
+    ] (cc1) {Carrier\\ Circuit};
+    \node [
+        draw,
+        fill=OrangeRed,
+        text width=2.5cm,
+        minimum height=1.2cm,
+        inner sep=0.3cm,
+        align=center,
+        right=2cm of cc1
+    ] (tm) {Transmission\\ Medium\\ (Channel)};
+    \node [
+        draw,
+        fill=SkyBlue,
+        text width=2cm,
+        minimum height=1.2cm,
+        inner sep=0.3cm,
+        align=center,
+        right=2cm of tm
+    ] (cc2) {Carrier\\ Circuit};
+    \node [
+        draw,
+        fill=SkyBlue,
+        text width=2cm,
+        minimum height=1.2cm,
+        inner sep=0.3cm,
+        align=center,
+        right=1cm of cc2
+    ] (sp2) {Signal\\ Processing};
+    %
+    \draw[<-] (sp1.west) -- ++ (-3, 0) node[at end, anchor=west, below right, label={[at end, above right, align=left]Information\\ Input}] {\(m\left( t \right)\)};
+    \draw[->] (sp1.east) -- (cc1.west);
+    %
+    \draw[->] (cc1.east) -- (tm.west) node[midway, below] {\(s\left( t \right)\)};
+    \draw[<-] (tm.north) -- ++ (0, 1.5) node[at end, anchor=south, above, text width=1cm, align=center] {Noise\\\(n\left( t \right)\)};
+    \draw[->] (tm.east) -- (cc2.west) node[midway, below] {\(r\left( t \right)\)};
+    %
+    \draw[->] (cc2.east) -- (sp2.west);
+    \draw[->] (sp2.east) -- ++ (3, 0) node[at end, anchor=east, below left, label={[at end, above left, align=right]Information\\ Output}] {\(\hat{m}\left( t \right)\)};
+    %
+    \draw[decorate,decoration={calligraphic brace,mirror,amplitude=0.3cm,raise=0.2cm},line width=0.03cm] (sp1.south west) -- (cc1.south east) node[midway, below=0.5cm] {Transmitter};
+    \draw[decorate,decoration={calligraphic brace,mirror,amplitude=0.3cm,raise=0.2cm},line width=0.03cm] (cc2.south west) -- (sp2.south east) node[midway, below=0.5cm] {Receiver};
+\end{tikzpicture}
+\end{document}