comparison draft.tex @ 39:f8849c5b18a0

Content analysis/Sound Categorisation

       informative of notes at different periodicities (\ie hypothetical
       bar lengths) and phases (\ie positions within a bar).
       }
     \end{fig}
 
-	\subsection{Content analysis/Sound Categorisation}.  
-        Overview of of information-theoretic approaches to music content analysis.
+    \subsection{Content analysis/Sound Categorisation}.
+    Using analogous definitions of differential entropy, the methods outlined in the previous section are equally applicable to continuous random variables. In the case of music, where expressive properties such as dynamics, tempo, timing and timbre are readily quantified on a continuous scale, the information dynamic framework thus may also be considered.
+
+    In \cite{Dubnov2006}, Dubnov considers the class of stationary Gaussian processes. For such processes, the entropy rate may be obtained analytically from the power spectral density of the signal, allowing the multi-information rate to be subsequently obtained. Local stationarity is assumed, which may be achieved by windowing or change point detection \cite{Dubnov2008}. %TODO mention non-gaussian processes extension
+    Similarly, the predictive information rate may be computed using a Gaussian linear formulation CITE. In this view, the PIR is a function of the correlation  between random innovations supplied to the stochastic process.
+    %Dubnov, MacAdams, Reynolds (2006)
+    %Bailes and Dean (2009)
+
         \begin{itemize}
-            \item Continuous domain information 
-						\item Audio based music expectation modelling
-            \item Proposed model for Gaussian processes      
+            \item Continuous domain information
+                        \item Audio based music expectation modelling
+            \item Proposed model for Gaussian processes
         \end{itemize}
     \emph{Peter}
 
 
 \subsection{Beat Tracking}