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08-00-ACA-Intensity.tex
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08-00-ACA-Intensity.tex
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% move all configuration stuff into includes file so we can focus on the content
\input{include}
\subtitle{module 8.0: intensity}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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?arnumber=6331121}{Chapter 4~---~Intensity}: pp.~71--78
chapter~8
\end{block}
\begin{itemize}
\item \textbf{lecture content}
\begin{itemize}
\item quick overview: human perception of loudness
\item intensity related features
\end{itemize}
\bigskip
\item<2-> \textbf{learning objectives}
\begin{itemize}
\item discuss level and loudness
\item list and describe typical intensity related low level features
\end{itemize}
\end{itemize}
\inserticon{directions}
\end{frame}
\section[intro]{introduction}
\begin{frame}{intensity, magnitude \& loudness}{introduction}
\begin{columns}
\column{0.6\linewidth}
\begin{itemize}
\item intensity-related descriptors \textbf{commonly used}
\begin{itemize}
\item waveform view
\item level monitoring (PPM, VU,\ldots)
\end{itemize}
\end{itemize}
\column{0.4\linewidth}
\begin{figure}%
\includegraphics[width=\columnwidth]{Waveform}%
\vspace{8mm}
\includegraphics[width=\columnwidth]{graph/ppmulator}%
\end{figure}
\end{columns}
\pause
\bigskip
\bigskip
\bigskip
\textbf{related terms}: magnitude $\bullet$ intensity $\bullet$ envelope $\bullet$ level $\bullet$ volume $\bullet$ velocity $\bullet$ loudness
\end{frame}
\section[perception]{loudness perception}
\begin{frame}{intensity, magnitude \& loudness}{human perception 1/2}
perception has non-linear relation to magnitude/RMS:
\begin{itemize}
\item model: logarithmic relation
\begin{equation*}
v_\mathrm{dB}(n) = 20\cdot\log_{10}\left(\frac{v(n)}{v_0}\right)
\end{equation*}
\begin{itemize}
\item $v_0$: reference constant (\unit[0]{dB} point)
\begin{itemize}
\item digital: $v_0 = 1$ $\Rightarrow \unit{dBFS}$
\item sound pressure $v_0 = 20\cdot10^{-6}$ $\Rightarrow \unit{dBSPL}$
\end{itemize}
\smallskip
\item scaling factor: \unit[1]{dB} $\approx$ JNDL for sound pressure level
\end{itemize}
\end{itemize}
\end{frame}
\begin{frame}{intensity, magnitude \& loudness}{side note: level computation}
\begin{itemize}
\item[] if $v(n) = 0\quad\Rightarrow$: computation of $\log_{10}(0)$
\end{itemize}
\begin{columns}
\column{.4\textwidth}
\begin{itemize}
\item<2-> \textbf{work-arounds}
\begin{enumerate}[a]
\item add constant $\epsilon$
\begin{equation*}
v_\mathrm{dB}(n) = 20\cdot\log_{10}(v(n) + \epsilon)
\end{equation*}
\item<3-> add \textbf{if} statement
\begin{equation*}
v_\mathrm{trunc}(n) = \left\{
\begin{array}{ll}
v(n), & \text{if } v(n) \geq \epsilon \\
\epsilon, & \text{otherwise }
\end{array}
\right.
\end{equation*}
\end{enumerate}
\end{itemize}
\column{.6\textwidth}
\only<2>{ %\vspace{-6mm}
\figwithmatlab{LogEpsilon}}
\end{columns}
\end{frame}
\begin{frame}{intensity, magnitude \& loudness}{human perception 2/2}
\only<1-2>{
\begin{itemize}
\item decibel scale is \textit{not} loudness scale:
\begin{itemize}
\item equal-sized steps on the decibel scale not perceived as equal-sized loudness steps
\end{itemize}
\bigskip
\item<2> perceptual phenomenon loudness depends on
\begin{itemize}
\item frequency
\item cochlear resolution
\item masking effects
\end{itemize}
\end{itemize}
}
\only<3>{
\figwithmatlab{LoudnessWeighting}
}
\end{frame}
\section[music]{loudness in music}
\begin{frame}{intensity, magnitude \& loudness}{dynamics in music}
\begin{itemize}
\item \textbf{score}:
\begin{itemize}
\item only several rough dynamic steps,e.g.:\\ \emph{\textbf{pp}}, \textit{\textbf{p}}, \emph{\textbf{mf}}, \emph{\textbf{f}}, \emph{\textbf{ff}}
\item<1-> comparably vague instructions on volume modifications, e.g.:\\ \textsl{crescendo}, \textsl{decrescendo}, \emph{\textbf{sf}}
\item<1-> dynamics influenced by
\begin{itemize}
\item instrumentation
\item timbre
\item number of voices
\item context and musical tension
\end{itemize}
\end{itemize}
\smallskip
\item<2-> \textbf{MIDI}:
\begin{itemize}
\item $128$ velocity steps
\item no standardized relation to magnitude, power, \ldots
\end{itemize}
\end{itemize}
\end{frame}
\section[features]{loudness features}
\begin{frame}{intensity, magnitude \& loudness}{features: root mean square 1/2}
\vspace{-6mm}
\begin{equation*}
\input{eq/Llf_Rms}
\end{equation*}
\only<2>{
\begin{itemize}
\item value of this feature for the hypothetical prototype signals
\begin{itemize}
\item silence
\item sinusoidal (Amplitude $A$)
%\item rect.\ white noise (Amplitude $A$)
\end{itemize}
\end{itemize}
}
\only<3>{
\vspace{-4mm}
\figwithref{FeatureTimeRms}{matlab source: \href{https://github.com/alexanderlerch/ACA-Plots/blob/master/matlab/plotFeatures.m}{matlab/plotFeatures.m}}
}
\vspace{50mm}
\end{frame}
\begin{frame}{intensity, magnitude \& loudness}{features: root mean square 2/2}
\textbf{common variants} (sample processing only):
\begin{itemize}
\item<1-> reduce computational complexity
\begin{footnotesize}
\begin{eqnarray*}
v^2_{\mathrm{RMS}}(n) &=& \frac{x(i_{\mathrm{e}}(n))^2 - x(i_{\mathrm{s}}(n-1))^2}{i_{\mathrm{e}}(n)-i_{\mathrm{s}}(n) + 1} + v^2_{\mathrm{RMS}}(n-1) \\
v_{\mathrm{RMS}}(n) &=& \sqrt{v^2_{\mathrm{RMS}}(n)}
\end{eqnarray*}
\end{footnotesize}
\smallskip
\item<2-> single pole approximation
\begin{footnotesize}
\begin{eqnarray*}
v_\mathrm{tmp}(i) &=& \alpha\cdot v_\mathrm{tmp}(i-1) + (1-\alpha)\cdot x(i)^2\\
v^*_{\mathrm{RMS}}(i) &=& \sqrt{v_\mathrm{tmp}(i)}
\end{eqnarray*}
\end{footnotesize}
\end{itemize}
\end{frame}
\begin{frame}{intensity, magnitude \& loudness}{features: weighted root mean square}
\begin{columns}
\column{0.4\linewidth}
\vspace{-8mm}
\begin{figure}
\centering
\input{pict/lowlevelfeatures_rmsblock}
\end{figure}
$H(z)$:
\begin{itemize}
\item A, B, C weighting
\item RLB (BS.1770)
\item \ldots
\end{itemize}
\column{0.6\linewidth}
\only<2->{
\figwithmatlab{LoudnessWeighting}
}
\end{columns}
\end{frame}
\begin{frame}{intensity, magnitude \& loudness}{features: peak envelope (max)}
\vspace{-5mm}
\begin{equation*}
v_{\mathrm{Peak}}(n) = \max_{i_{\mathrm{s}}(n) \leq i \leq i_{\mathrm{e}}(n)}{|x(i)|}
\end{equation*}
\only<2>{
\vspace{-3mm}
\figwithref{FeatureTimePeakEnvelope}{matlab source: \href{https://github.com/alexanderlerch/ACA-Plots/blob/master/matlab/plotFeatures.m}{matlab/plotFeatures.m}}
}
\vspace{50mm}
\end{frame}
\begin{frame}{intensity, magnitude \& loudness}{features: peak envelope (PPM) 1/2}
\begin{figure}
\centering
\input{pict/lowlevelfeatures_ppm}
\end{figure}
\only<1>{\vspace{30mm}}
\only<2->{
\begin{itemize}
\only<2-3>{
\item \textbf{release state} ($|x(i)| < v_{\mathrm{PPM}}(i-1)\Rightarrow\lambda = \alpha_\mathrm{RT}$)
\invisible<2>{
\begin{eqnarray*}
v_{\mathrm{PPM}}(i) &=& v_{\mathrm{PPM}}(i-1) - \alpha_\mathrm{RT}\cdot v_{\mathrm{PPM}}(i-1)\nonumber\\
&=& (1-\alpha_\mathrm{RT})\cdot v_{\mathrm{PPM}}(i-1)
\end{eqnarray*}
}
}
\only<4-5>{
\item \textbf{attack state} ($|x(i)| \geq v_{\mathrm{PPM}}(i-1)\Rightarrow\lambda = 0$)
\invisible<4>{
\begin{eqnarray*}
v_{\mathrm{PPM}}(i) &=& \alpha_\mathrm{AT}\cdot\big(|x(i)| - v_{\mathrm{PPM}}(i-1)\big) + v_{\mathrm{PPM}}(i-1)\nonumber\\
&=& \alpha_\mathrm{AT}\cdot |x(i)| + (1-\alpha_\mathrm{AT})\cdot v_{\mathrm{PPM}}(i-1)
\end{eqnarray*}
}
}
\end{itemize}
}
\end{frame}
\begin{frame}{intensity, magnitude \& loudness}{features: peak envelope (PPM) 2/2}
\vspace{-3mm}
\figwithref{FeatureTimePeakEnvelope}{matlab source: \href{https://github.com/alexanderlerch/ACA-Plots/blob/master/matlab/plotFeatures.m}{matlab/plotFeatures.m}}
\vspace{-2mm}
\begin{itemize}
\item gold: max per block
\item blue: PPM
\end{itemize}
\end{frame}
\begin{frame}{intensity, magnitude \& loudness}{features: zwicker loudness}
\vspace{-3mm}
\begin{figure}
\scalebox{.8}
{
\centering
\input{pict/lowlevelfeatures_zwicker}
}
\end{figure}
\vspace{-5mm}
\uncover<2->{
\begin{itemize}
\item
\only<2>{ outer ear transfer function\footfullcite{hammershoi_methods_2002}
\begin{figure}
\includegraphics[scale=.25]{graph/OETF}
\end{figure}
}
\only<3>{ excitation patterns\footfullcite{schleske_website}
\begin{figure}
\includegraphics[scale=.5]{graph/excitationpatterns}
\end{figure}
}
\only<4>{ specific loudness\footfullcite{specloudness_website}
\begin{figure}
\includegraphics[scale=.3]{graph/specificloudness}
\end{figure}
}
\only<5>{ overall loudness
\[ v_\mathrm{loud} = \sum_{\forall i} z_i\]
}
\end{itemize}
}
\end{frame}
\begin{frame}{intensity, magnitude \& loudness}{derived features}
\begin{itemize}
\item number or ratio of pauses
\item dynamic range
\item other statistical features from (RMS) histogram
\item \ldots
\end{itemize}
\end{frame}
\section{summary}
\begin{frame}{summary}{lecture content}
\begin{itemize}
\item \textbf{loudness perception}
\begin{itemize}
\item nonlinear relation to magnitude or power
\item depends also on frequency, level, and signal (masking)
\end{itemize}
\bigskip
\item \textbf{typical features}
\begin{itemize}
\item derived from envelope (peak, RMS, weighted RMS)
\item derived from histogram (range, mode)
\end{itemize}
\end{itemize}
\inserticon{summary}
\end{frame}
\end{document}