03-03-04-ACA-Input-TF-Filterbanks.tex

% move all configuration stuff into includes file so we can focus on the content
\input{include}


\subtitle{module 3.3.4: time-frequency representations~---~filterbanks}

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\begin{document}
    % generate title page
	\input{include/titlepage}

    \section[overview]{lecture overview}
        \begin{frame}{introduction}{overview}
            \begin{block}{corresponding textbook section}
                    %\href{http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6331119&}{Chapter 2~---~Fundamentals}: pp.~24--26
                    section~3.3.4
            \end{block}

            \begin{itemize}
                \item   \textbf{lecture content}
                    \begin{itemize}
                        \item   gammatone filterbank
                        \item   resonance filterbank
                    \end{itemize}
                \bigskip
                \item<2->   \textbf{learning objectives}
                    \begin{itemize}
                        \item   explaining the principles of (auditory) filterbanks
                    \end{itemize}
            \end{itemize}
            \inserticon{directions}
        \end{frame}
        
    \section[intro]{introduction}
        \begin{frame}{auditory filterbanks}{introduction}
            FT and related transforms are bad models of physiological properties of the human ear:
                \begin{itemize}
                    \item   frequency resolution (critical bands)
                    \item   frequency scale (pitch resolution)
                    \item   loudness \& masking
                    \item   event perception \&  time integration
                \end{itemize}
            
            \smallskip
            $\Rightarrow$ \textbf{auditory filterbanks}
            
            \pause
            \bigskip
            not as widely used as one might think because
            
            \begin{enumerate}
                \item<3->	computationally inefficient
                \item<3->	analysis only: no invertibility (mostly)
                \item<3->	not proven to be superior
            \end{enumerate}
        \end{frame}	
        
    \section[gammatone]{Gammatone Filterbank}
        \begin{frame}{auditory filterbanks}{gammatone filterbank}
            \vspace{-6mm}
            \begin{equation*}
                h(i) = \frac{ a \cdot\left(\nicefrac{i}{f_{\mathrm{S}}}\right)^{\mathcal{O}-1}\cdot \cos\left( 2\pi \cdot f_{\mathrm{c}} \frac{ i}{f_{\mathrm{S}}} \right) }{\e^{\nicefrac{2\pi i \Delta f}{f_{\mathrm{S}}}}}
            \end{equation*}
            \vspace{-4mm}
            \figwithmatlab{Gammatone}
        \end{frame}	
        
    \section[resonance]{Other Filterbanks}
        \begin{frame}{other filterbanks}{resonance filterbank}
            \figwithmatlab{ResonanceFilterbank}
        \end{frame}	

    \section{summary}
        \begin{frame}{summary}{lecture content}
            \begin{itemize}
                \item      \textbf{filterbank-based frequency transforms}
                    \begin{itemize}
                        \item   possibly good model of human physiology
                        \item   high time resolution
                        \item   not invertible and inefficient
                        \item   not proven to be superior
                    \end{itemize}
            \end{itemize}
            \inserticon{summary}
        \end{frame}
\end{document}