\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\author{Lilly Elizabeth Alice Doye 29532183 stad1g17}
\title{MATH2047 2018-19 Coursework 1: Fourier series and transform}
\begin{document}

    \maketitle

    \section{[14 marks]}
        \subsection{[4 marks]}
            \begin{equation}
                y(t):=Zx(t)cos(\omega_0 t)
            \end{equation}
        \subsection{[4 marks]}
            \begin{equation}
                y(t):=Zx(t)cos(\omega_0 t+\theta)
            \end{equation}
        \subsection{[6 marks]}
            \begin{equation}
                y(t):=Zx(t-T_0)cos(\omega_0 t)
            \end{equation}

    \section{[12 marks]}
        \subsection{[4 marks]}
            \begin{equation}
                \mathcal{F}(\overleftarrow{v})(\omega)=\mathcal{F}(v)(-\omega)
            \end{equation}
        \subsection{[4 marks]}
            \begin{equation}
                p(t):=(g*v)(t)
            \end{equation}
            \begin{equation}
                u(t):=(g*\overleftarrow{v})(t)
            \end{equation}
        \subsection{[4 marks]}
            \begin{equation}
                u(t)=p(-t)
            \end{equation}

    \section{[18 marks]}
        \subsection{[6 marks]}
            \begin{equation}
                \begin{bmatrix}
                    \hat{f}_0\\
                    \hat{f}_1\\
                    \vdots\\
                    \hat{f}_{N-1}\\
                \end{bmatrix}
                =W
                \begin{bmatrix}
                    f_0\\
                    f_1\\
                    \vdots\\
                    f_{N-1}\\
                \end{bmatrix}
            \end{equation}
        \subsection{[4 marks]}

        \subsection{[4 marks]}
            \begin{equation}
                \{f'_0,f'_1,f'_2,f'_3,\}:=\{f_3,f_0,f_1,f_2\}
            \end{equation}
        \subsection{[4 marks]}

        \footnote{Made with MATH2047 template by Lilly Doye}
\end{document}