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Updated README

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1 parent 7b8ab71 commit 21408f7319d16a8951ac5a140225885b5f431981 @Cadair Cadair committed Apr 19, 2012
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2 README
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-DUMMY README
+A Hilbert Haung Transform package, should perform EMD as well as generate a Hilbert Spectra.
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134 scipy.tex
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-% This is the source code for my presentation on pyhht at SciPy India 2011 held in Mumbai in Dec 2011
-
-\documentclass[xcolor=dvipsnames]{beamer}
-\usetheme{Warsaw}
-\usecolortheme[named=Blue]{structure}
-\usepackage{graphics}
-
-\title{pyhht: A Python Toolbox for the Hilbert-Huang Transform}
-\author{Jaidev Deshpande \\ deshpande.jaidev@gmail.com}
-\institute{VIIT, Pune}
-\date{December 5, 2011}
-
-
-\begin{document}
-
-\begin{frame}
-\titlepage
-\end{frame}
-
-
-
-\begin{frame}{Introduction - Why this talk?}
-\begin{itemize}
-\item Introducing HHT
-\item An additional view of nonlinear and nonstationary phenomena
-\item HHT is almost entirely algorithmic
-\item It needs more math
-\item I need an audience
-\end{itemize}
-\end{frame}
-
-%3
-\begin{frame}{Motivation for the HHT}
-\begin{itemize}
-\item What's the Hilbert Transform good for?
-\begin{enumerate}
-\item Analytical signals
-\item Instantanous frequency
-\end{enumerate}
-\item Meaningful representations of data
-\item A check against harmonics
-\item Feature extraction
-\end{itemize}
-\end{frame}
-
-%4
-\begin{frame}{The Hilbert-Huang Transform}
-\begin{itemize}
-\item HHT = Empirical Mode Decomposition + Hilbert Spectral Analysis
-\item EMD: breaks a wideband signal down into piecewise narrowband signals, called IMFs
-\item Intrinsic Mode Functions:
-\begin{enumerate}
-\item Well behaved Hilbert Transforms
-\item Piecewise stationary
-\item Almost purely AM/FM
-\end{enumerate}
-\end{itemize}
-\end{frame}
-
-%5
-\begin{frame}{Intrinsic Mode Functions}
-\begin{definition}
-A function is called an Intrinsic Mode Function if
-
-\begin{enumerate}
-\item the number of zero crossings and local extrema in the function differ at most by unity (takes care of localized oscillations)
-\item the local mean of the enevelopes described by the local maxima and the local minima is zero at all times (required for meaningful instantaneous frequencies)
-\end{enumerate}
-\end{definition}
-
-\end{frame}
-
-%6
-\begin{frame}{Empirical Mode Decomposition}
-\begin{enumerate}
-\item Find all local extrema in the signal
-\item Join the maxima and minima with separate cubic splines, creating an upper and a lower envelope
-\item Calculate the mean of the envelopes
-\item Subtract mean from original signal
-\item Repeat steps 1-4 until the result is an IMF
-\item Subtract this IMF from the original signal
-\item Repeat steps 1-6 till there are no more IMFs left in the signal
-\end{enumerate}
-\end{frame}
-%
-%%7
-\begin{frame}{Hilbert Spectral Analysis}
-Analytical signals from the IMFs:
-\begin{equation}
-z(t)=x(t)+i*y(t)
-\end{equation}
-Instantaneous phase can be calculated as:
-\begin{equation}
-\theta = \tan ^{-1} {\frac{y(t)}{x(t)}}
-\end{equation}
-Instantaneous frequency, therefore:
-\begin{equation}
-\omega _{i}=\frac{d \theta}{dt}
-\end{equation}
-The original array is the real part of:
-\begin{equation}
-X(t)=\sum _{j=1} ^{N} x_{j}(t) \exp (i\int \omega_{j} (t).dt)
-\end{equation}
-\end{frame}
-%
-%%8
-\begin{frame}{Comparison with Fourier and Wavelet}
-%\includegraphics[scale=0.3]{Screenshot}
-\end{frame}
-%
-%%9
-\begin{frame}{Heuristics for HHT}
-\begin{itemize}
-\item Stoppage criteria for sifting
-\item Screening tools for IMFs based on statistical moments, information theoretic measures, etc
-\item Alternatives to sifting like SVD, ICA
-\item Better interpolation schemes
-\end{itemize}
-\end{frame}
-
-\begin{frame}{What Would be Awesome}
-\begin{itemize}
-\item Speeding it up
-\item A quantitative analysis of the EMD as a feature extraction, data compression method
-\item Use of wavelets as a handle on the HHT
-\item Establishing it as a veritable generalization of the Fourier method
-\end{itemize}
-\end{frame}
-%
-\begin{frame}
-Thank You
-\end{frame}
-
-\end{document}

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