HHT.rar_hht_希尔伯特变换_软件设计/软件工程下载-pudn.com

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/622bb5b615da9b288bc9a9ee/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622bb5b615da9b288bc9a9ee/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h2 y3 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h2 y4 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h2 y5 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h2 y6 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h2 y7 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h2 y8 ff1 fs0 fc0 sc0 ls1 ws1">Signal filtering, Wavelet transf<span class="ls2 ws2">orm<span class="_ _0"></span>, Hilbert-Huang transform </span></div><div class="t m0 x2 h2 y9 ff1 fs0 fc0 sc0 ls3 ws3">En jämförelse </div><div class="t m0 x2 h2 ya ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 yb ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 yc ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 yd ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 ye ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 yf ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 y10 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 y11 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 y12 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 y13 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 y14 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 y15 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x2 h2 y16 ff1 fs0 fc0 sc0 ls4 ws4">Nazar Dino mohammed </div><div class="t m0 x2 h2 y17 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y18 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y19 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1a ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1b ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1c ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1d ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1e ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1f ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y20 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y21 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y22 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y23 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y24 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y25 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y26 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y27 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y28 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y29 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y2a ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y2b ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y2c ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y2d ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y2e ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y2f ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y30 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y31 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y32 ff2 fs0 fc0 sc0 ls0 ws0"> </div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622bb5b615da9b288bc9a9ee/bg2.jpg"><div class="t m0 x3 h3 y33 ff2 fs0 fc0 sc0 ls2 ws2">Sammanfattning </div><div class="t m0 x3 h3 y34 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y3 ff1 fs0 fc0 sc0 ls4 ws5">Detta examensarbete behandlar och jämför DWT (Discrete Wavelet Transform<span class="_ _0"></span>) och </div><div class="t m0 x3 h2 y4 ff1 fs0 fc0 sc0 ls2 ws2">HHT(Hilbert-Huang Transform). I många sammanhangarer och tillämpningar, tid- </div><div class="t m0 x3 h2 y5 ff1 fs0 fc0 sc0 ls5 ws6">frekvens representation av en signal är vi<span class="ls0 ws7">ktig och betydelsefull. Tid- frekvens </span></div><div class="t m0 x3 h2 y6 ff1 fs0 fc0 sc0 ls4 ws8">analyser ger de mest betydelsefulla inform<span class="ls6 ws9">ationer om<span class="_ _0"></span> signalen frekvens, deras styrka </span></div><div class="t m0 x3 h3 y7 ff1 fs0 fc0 sc0 ls4 ws5">och hur de ändras sig med tiden. <span class="ff2 ls0 ws0"> </span></div><div class="t m0 x1 h2 y8 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y9 ff1 fs0 fc0 sc0 ls5 ws6">Traditionella metoder som Fouier transfor<span class="ls2 ws2">m, kan ge bara en frekvens baserade </span></div><div class="t m0 x3 h2 ya ff1 fs0 fc0 sc0 ls0 ws0">representation av signalen och <span class="ls7 wsa">kan tillämpas bara på linjä</span><span class="wsb">ra processer. De flesta </span></div><div class="t m0 x3 h2 yb ff1 fs0 fc0 sc0 ls4 wsc">processer i verkligheten är icke linjär och ic<span class="ls5 ws6">ke stationära processer och därför andra </span></div><div class="t m0 x3 h2 yc ff1 fs0 fc0 sc0 ls1 wsd">metoder som kan tillämpas på alla signaler och ger en tid- fr<span class="_ _0"></span>ekvens approximation av </div><div class="t m0 x3 h2 yd ff1 fs0 fc0 sc0 ls8 wsc">signaler, är nödvändiga. DWT oc<span class="ls9 ws2">h HHT är några av de metoder som kan användas för </span></div><div class="t m0 x3 h2 ye ff1 fs0 fc0 sc0 lsa wse">detta syfte. </div><div class="t m0 x1 h2 yf ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y10 ff1 fs0 fc0 sc0 ls3 ws3">Ett annat viktig del av signa<span class="ls7 wsa">l processning handlar om kla<span class="_ _0"></span><span class="ls5 ws6">ssificering av signaler och </span></span></div><div class="t m0 x3 h2 y11 ff1 fs0 fc0 sc0 ls3 wsf">känna igen signaler och detta kan göras me<span class="ws10">d PCA (Principal component analysis) och </span></div><div class="t m0 x3 h2 y12 ff1 fs0 fc0 sc0 ls2 ws2">NN (Neural network). Men innan dess måst<span class="ls4 ws8">e viktigaste information om tid och </span></div><div class="t m0 x3 h2 y13 ff1 fs0 fc0 sc0 ls8 ws11">frekvens av signaler best<span class="ls4 ws12">ämmas och vi kan göra detta med DWT och HHT. Vi tar </span></div><div class="t m0 x3 h2 y14 ff1 fs0 fc0 sc0 ls2 ws2">några riktiga signaler (infrasound signaler)och<span class="ls4 ws5"> tillämpar de olika metoder och jämf<span class="_ _0"></span>ör </span></div><div class="t m0 x3 h2 y15 ff1 fs0 fc0 sc0 ls1 ws0">dem. </div><div class="t m0 x3 h3 y35 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y36 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y18 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y19 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1a ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1b ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1c ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1d ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1e ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1f ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y20 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y21 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y22 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y23 ff2 fs0 fc0 sc0 ls0 ws0"> </div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>

<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622bb5b615da9b288bc9a9ee/bg3.jpg"><div class="t m0 x3 h3 y33 ff2 fs0 fc0 sc0 ls4 ws5">Abstract </div><div class="t m0 x3 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y3 ff1 fs0 fc0 sc0 ls9 ws3">In this work, we will compare the discrete wavelet transform<span class="_ _0"></span> (DWT) and Hilbert </div><div class="t m0 x3 h2 y4 ff1 fs0 fc0 sc0 ls8 ws13">Huang transform (HHT) as pre-processing t<span class="ls2 ws2">echniques for signal classification using </span></div><div class="t m0 x3 h2 y5 ff1 fs0 fc0 sc0 ls2 ws2">Neural Network. Time-frequency analysis <span class="lsb ws14">is important part <span class="ls4 ws5">of signal processing. </span></span></div><div class="t m0 x3 h2 y6 ff1 fs0 fc0 sc0 ls5 ws6">Time-frequency analysis is the process of de<span class="ls7 wsa">termining what freque<span class="ls6 ws15">ncies are present in<span class="_ _0"></span> </span></span></div><div class="t m0 x3 h2 y7 ff1 fs0 fc0 sc0 ls8 ws13">a signal, how strong they are and how <span class="ls2 ws16">they change over time. DWT and HHT </span></div><div class="t m0 x3 h2 y8 ff1 fs0 fc0 sc0 ls7 ws17">techniques, determine the different<span class="ls8 ws1"> frequencies in the signal. </span></div><div class="t m0 x1 h2 y9 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 ya ff1 fs0 fc0 sc0 ls2 ws2">Wavelet transform is common approach to<span class="ls4 ws8"> study time-frequency resolution in signal </span></div><div class="t m0 x3 h2 yb ff1 fs0 fc0 sc0 ls5 wsc">processing. Wavelet transform can be applie<span class="ls0 ws12">d to linear and non stationary processes </span></div><div class="t m0 x3 h2 yc ff1 fs0 fc0 sc0 ls0 ws0">while HHT can be applied to non linear processes and non sta<span class="ls2 ws2">tionary process. </span></div><div class="t m0 x1 h2 yd ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 ye ff1 fs0 fc0 sc0 ls2 wsf">The physical processes in the nature ar<span class="ws2">e usually non-linear <span class="ls0 ws0">and non-stationary. </span></span></div><div class="t m0 x3 h2 yf ff1 fs0 fc0 sc0 ls4 ws4">For example infrasound signals can be c<span class="ls5 ws18">onsidered non-linear and non-stationary </span></div><div class="t m0 x3 h2 y10 ff1 fs0 fc0 sc0 ls2 ws2">processes. In our experiments, we use <span class="ls5 ws6">infrasound signals from different events. </span></div><div class="t m0 x1 h2 y11 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y12 ff1 fs0 fc0 sc0 ls2 ws2">Classification and recognition of signals ar<span class="ls7 ws19">e important parts of signal processing and </span></div><div class="t m0 x3 h2 y13 ff1 fs0 fc0 sc0 ls7 wsa">they have many application such face recognition, fingerprin<span class="_ _0"></span>t matching, voice </div><div class="t m0 x3 h2 y14 ff1 fs0 fc0 sc0 ls7 ws12">recognition, to name a few. This can be done for example by methods like Neural </div><div class="t m0 x3 h2 y15 ff1 fs0 fc0 sc0 ls7 ws19">networks (NN), however before that, we need<span class="ls4 ws5"> to take the most significant inform<span class="_ _0"></span>ation </span></div><div class="t m0 x3 h2 y16 ff1 fs0 fc0 sc0 ls1 ws1">from signals like time and frequency. Both DW<span class="_ _0"></span>T and HHT are optimal methods for </div><div class="t m0 x3 h2 y17 ff1 fs0 fc0 sc0 ls0 ws1">this purpose .In this work we use some<span class="ls2 ws2"> real signals (inf<span class="ls5 ws6">rasound signals) and </span></span></div><div class="t m0 x3 h2 y37 ff1 fs0 fc0 sc0 ls8 ws1a">processing them with DWT, HHT and NN. </div><div class="t m0 x1 h2 y38 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y39 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y3a ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1c ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1d ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1e ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y1f ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y20 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y21 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y22 ff2 fs0 fc0 sc0 ls0 ws0"> </div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>

<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622bb5b615da9b288bc9a9ee/bg4.jpg"><div class="t m0 x3 h3 y33 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y3 ff1 fs0 fc0 sc0 lsc ws0"> </div><div class="t m0 x3 h4 y3b ff2 fs1 fc0 sc0 lsd ws1b">1 Introduction </div><div class="t m0 x3 h5 y3c ff3 fs0 fc1 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y3d ff1 fs0 fc0 sc0 ls1 ws7">The goal of our project is to compare th<span class="ls3 ws1c">e discrete wavelet transform (DWT) and </span></div><div class="t m0 x3 h2 y3e ff1 fs0 fc0 sc0 ls3 ws3">Hilbert Huang transform (HHT) as pre-proces<span class="ls0 ws0">sing techniques for si<span class="ls5 ws6">gnal classification </span></span></div><div class="t m0 x3 h2 y3f ff1 fs0 fc0 sc0 ls2 wsf">using Neural Network. We use infrasound si<span class="ls4 ws5">gnals from two events: sound of opening </span></div><div class="t m0 x3 h2 y40 ff1 fs0 fc0 sc0 ls4 ws5">doors and sound of cars. Before we test a<span class="ls1 ws8">nd processing signals, we will ex<span class="_ _0"></span>plain the </span></div><div class="t m0 x3 h2 y41 ff1 fs0 fc0 sc0 ls1 ws1d">mathematically bases of DWT and HHT tran<span class="_ _0"></span><span class="ls2 ws2">sforms and after that we will implement </span></div><div class="t m0 x3 h3 y42 ff1 fs0 fc0 sc0 ls1 ws1">the methods and see the results.<span class="ff2 ls0 ws0"> </span></div><div class="t m0 x3 h2 y43 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y44 ff1 fs0 fc0 sc0 ls4 ws5">In many applications, we need information about time and frequency of a signal. </div><div class="t m0 x3 h2 y45 ff1 fs0 fc0 sc0 ls4 ws5">Signal itself does not provide much informa<span class="ls2 ws2">tion and we need to find some m<span class="_ _0"></span>ethods to </span></div><div class="t m0 x3 h2 y46 ff1 fs0 fc0 sc0 ls9 ws1e">determine time-frequency re<span class="ls5 ws6">presentation of signal. </span></div><div class="t m0 x3 h2 y47 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y48 ff1 fs0 fc0 sc0 ls3 ws3">In mathematics, there are methods to descri<span class="ls2 ws1f">be a function (or signal) in the terms of </span></div><div class="t m0 x3 h2 y49 ff1 fs0 fc0 sc0 ls3 ws11">orthogonal bases functions. Fourier transf<span class="ls2 ws2">orms (FT), wavelet transform<span class="_ _0"></span>s (WT), </span></div><div class="t m0 x3 h2 y4a ff1 fs0 fc0 sc0 ls5 ws6">Hilbert-Huang transform (HHT) are exampl<span class="ls3 ws3">es of those methods to represent and </span></div><div class="t m0 x3 h2 y4b ff1 fs0 fc0 sc0 ls7 ws17">approximate functions. Fourier transforms <span class="ws11">(FT) and wavelet transform<span class="_ _0"></span>s (WT) are </span></div><div class="t m0 x3 h2 y4c ff1 fs0 fc0 sc0 ls3 ws3">based on Hilbert space and inner product. Th<span class="ls0 ws0">ese tools have been used for many years. </span></div><div class="t m0 x3 h2 y4d ff1 fs0 fc0 sc0 ls1 wsf">The bases function in WT and FT are complete, orthonormal bases or </div><div class="t m0 x3 h2 y4e ff1 fs0 fc0 sc0 ls3 ws3">overcomplete.[see Appendix A] </div><div class="t m0 x3 h2 y4f ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y50 ff1 fs0 fc0 sc0 ls2 ws2">Wavelet has many applications and especi<span class="lse ws20">ally the Discre<span class="_ _0"></span>te Wavelet Transform </span></div><div class="t m0 x3 h2 y51 ff1 fs0 fc0 sc0 ls4 ws5">(DWT) is commonly used in engineering, com<span class="_ _0"></span>puter science and scientific research. </div><div class="t m0 x3 h2 y52 ff1 fs0 fc0 sc0 ls2 ws2">Generally DWT is used for data compressi<span class="ls5 ws6">on; one example of <span class="ls0 ws0">using DWT is JPEG </span></span></div><div class="t m0 x3 h2 y53 ff1 fs0 fc0 sc0 ls1 wsc">2000 which is image compression.The software im<span class="_ _0"></span>plementation of DWT is easy, </div><div class="t m0 x3 h2 y54 ff1 fs0 fc0 sc0 ls6 ws11">especially in the matlab. One can also im<span class="_ _0"></span>pl<span class="ls9 ws1e">ement DWT easily in other program<span class="_ _0"></span>s, such </span></div><div class="t m0 x3 h2 y55 ff1 fs0 fc0 sc0 ls0 ws0">C++ or python. </div><div class="t m0 x3 h2 y56 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y57 ff1 fs0 fc0 sc0 ls1 ws19">In the many other areas like: seismic geophys<span class="ws21">ics, general sign<span class="_ _0"></span>al processes, speech </span></div><div class="t m0 x3 h2 y58 ff1 fs0 fc0 sc0 ls4 ws15">recognition, computer graphic, etc. DWT <span class="ls7 wsa">have been powerful tool to analyse and </span></div><div class="t m0 x3 h2 y59 ff1 fs0 fc0 sc0 ls5 ws6">process data. </div><div class="t m0 x3 h2 y5a ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y5b ff1 fs0 fc0 sc0 ls0 ws0">The Hilbert-Huang transform (HHT) is an<span class="ls4 ws5"> empirical method to analyse data. The </span></div><div class="t m0 x3 h2 y5c ff1 fs0 fc0 sc0 lsf ws22">traditionally m<span class="_ _0"></span>ethods like WT and FT can only <span class="ls3 ws3">apply to linear proces<span class="_ _0"></span>ses and has been </span></div><div class="t m0 x3 h2 y5d ff1 fs0 fc0 sc0 ls2 ws2">used in many years for processing data. <span class="ls8 wsa">But question is what can we do about non-</span></div><div class="t m0 x3 h2 y5e ff1 fs0 fc0 sc0 lsb ws22">linear processes? </div><div class="t m0 x1 h2 y5f ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y60 ff1 fs0 fc0 sc0 ls2 ws2">Almost all processes in the nature are <span class="ls3 wsf">non linear and non stationary, and to analyze </span></div><div class="t m0 x3 h2 y61 ff1 fs0 fc0 sc0 ls2 wsb">this kind of signals, we need other appro<span class="wsd">aches. The need of methods, which can apply </span></div><div class="t m0 x3 h2 y62 ff1 fs0 fc0 sc0 ls2 wsf">to non linear processes, is necessary. HHT <span class="ls4 ws5">is one of those methods, which has been </span></div><div class="t m0 x3 h2 y63 ff1 fs0 fc0 sc0 ls5 ws6">used in recent years. This method has <span class="ls8 ws1">ability to processing both non linear and non </span></div><div class="t m0 x3 h2 y64 ff1 fs0 fc0 sc0 ls4 wsb">stationary processes and that show<span class="ls5 ws6">s the importance and power of HHT. </span></div><div class="t m0 x1 h2 y65 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y66 ff1 fs0 fc0 sc0 ls1 ws19">HHT has very simple algorithm to understand an<span class="_ _0"></span><span class="ls3 ws3">d this algorithm can be applied easily </span></div><div class="t m0 x3 h2 y67 ff1 fs0 fc0 sc0 ls3 ws3">to analyze signals. However there are a lot of<span class="ls2 ws2"> works to be done. Most work with the </span></div><div class="t m0 x3 h2 y68 ff1 fs0 fc0 sc0 ls3 wsf">HHT was related to its application and there <span class="ls1 ws1">is not so much work about m<span class="_ _0"></span>athematical </span></div><div class="t m0 x3 h2 y69 ff1 fs0 fc0 sc0 ls0 ws0">and theoretical foundation of HHT. </div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>

<div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622bb5b615da9b288bc9a9ee/bg5.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y2 ff1 fs0 fc0 sc0 ls4 ws5">Table 1 presents a summary of methods and their comparison: </div><div class="t m0 x3 h2 y3 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y4 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y5 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y6 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h6 y6a ff1 fs2 fc0 sc0 ls10 ws23">Table 1: Fourier, Wa<span class="_ _0"></span>velet and Hilbert-Huang T<span class="_ _0"></span>ransforms </div><div class="t m0 x3 h6 y6b ff1 fs2 fc0 sc0 ls11 ws24"> Fourier <span class="_ _1"></span>Wavelet <span class="_ _2"></span>Hilbert </div><div class="t m0 x3 h6 y6c ff1 fs2 fc0 sc0 ls12 ws25">Basis <span class="_ _3"> </span>a priori <span class="_ _4"> </span>a priori <span class="_ _4"> </span>Adaptive </div><div class="t m0 x3 h6 y6d ff1 fs2 fc0 sc0 ls13 ws26">frequency con<span class="_ _0"></span>volution: </div><div class="t m0 x4 h6 y6e ff1 fs2 fc0 sc0 ls14 ws27">global uncertainty </div><div class="t m0 x5 h6 y6d ff1 fs2 fc0 sc0 ls15 ws0">convolution: </div><div class="t m0 x5 h6 y6e ff1 fs2 fc0 sc0 ls16 ws28">regional uncertainty </div><div class="t m0 x6 h6 y6d ff1 fs2 fc0 sc0 ls17 ws0">different<span class="_ _0"></span>iation: </div><div class="t m0 x6 h6 y6e ff1 fs2 fc0 sc0 ls18 ws29">local uncertainty </div><div class="t m0 x3 h6 y6f ff1 fs2 fc0 sc0 ls19 ws2a">Presentation <span class="_ _5"> </span>energy-freque<span class="_ _0"></span>ncy <span class="_ _6"> </span>energy-time-freque<span class="_ _0"></span>ncy <span class="_ _7"> </span>energy-time-freque<span class="_ _0"></span>ncy </div><div class="t m0 x3 h6 y70 ff1 fs2 fc0 sc0 ls1a ws2b">Nonlinear no <span class="_ _8"> </span>no <span class="_ _9"> </span>yes </div><div class="t m0 x3 h6 y71 ff1 fs2 fc0 sc0 ls1b ws2c">Nonstationary<span class="_ _0"></span> <span class="_ _a"> </span>no <span class="_ _b"> </span>yes <span class="_ _c"> </span>yes </div><div class="t m0 x3 h6 y72 ff1 fs2 fc0 sc0 ls1b ws0">Feature Extract<span class="_ _0"></span>ion <span class="_ _8"> </span>no <span class="_ _b"> </span>discrete :no </div><div class="t m0 x5 h6 y73 ff1 fs2 fc0 sc0 ls1c ws2d">continuous : yes </div><div class="t m0 x5 h6 y74 ff1 fs2 fc0 sc0 ls0 ws0"> </div><div class="t m0 x6 h6 y72 ff1 fs2 fc0 sc0 ls1d ws0">yes </div><div class="t m0 x3 h6 y75 ff1 fs2 fc0 sc0 ls1e ws2e">Theoretical base <span class="_ _d"> </span>theory complete <span class="_ _e"> </span>theory complete <span class="_ _e"> </span>empirical </div><div class="t m0 x3 h3 y76 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y77 ff1 fs0 fc0 sc0 ls9 ws17">First the Fourier transform, DWT and HHT w<span class="_ _0"></span><span class="ls1f ws2f">ill be explained in this chapter and after </span></div><div class="t m0 x3 h2 y78 ff1 fs0 fc0 sc0 ls6 ws8">that in chapter 2, the methods will be implemen<span class="_ _0"></span><span class="ls1 ws7">t. Finally in the chapter 3 the results of </span></div><div class="t m0 x3 h2 y79 ff1 fs0 fc0 sc0 ls6 ws30">the methods will be represented </div><div class="t m0 x3 h2 y7a ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y7b ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 y7c ff2 fs0 fc0 sc0 ls7 ws17">1.1 The Fourier transform </div><div class="t m0 x3 h2 y7d ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y7e ff1 fs0 fc0 sc0 ls3 ws21">The standard Fourier transf<span class="ls7 ws18">orm is presented in (1.1.1). <span class="fc1 ls0 ws0"> </span></span></div><div class="t m0 x7 h7 y7f ff1 fs3 fc0 sc0 ls0 ws0">(<span class="_ _f"></span><span class="ff3">Ff<span class="_ _10"> </span></span>)(</div><div class="t m1 x8 h8 y7f ff4 fs4 fc0 sc0 ls0 ws0">ω</div><div class="t m0 x9 h7 y7f ff1 fs3 fc0 sc0 ls0 ws0">)<span class="_ _10"> </span><span class="ff4">=</span></div><div class="t m0 x4 h7 y80 ff1 fs3 fc0 sc0 ls0 ws0">1</div><div class="t m0 xa h7 y81 ff1 fs3 fc0 sc0 ls0 ws0">2</div><div class="c xb y82 w2 h9"><div class="t m1 x0 h8 y83 ff4 fs4 fc0 sc0 ls0 ws0">π</div></div><div class="t m0 xc ha y7f ff3 fs3 fc0 sc0 ls0 ws0">dte</div><div class="t m0 xd hb y84 ff4 fs5 fc0 sc0 ls0 ws0">−<span class="_ _11"></span><span class="ff3">i</span></div><div class="t m2 xe hc y84 ff4 fs6 fc0 sc0 ls0 ws0">ω</div><div class="t m0 xf hb y84 ff3 fs5 fc0 sc0 ls0 ws0">t</div><div class="t m0 x10 h7 y7f ff3 fs3 fc0 sc0 ls0 ws0">f<span class="_ _10"> </span><span class="ff1">(<span class="_ _f"></span></span>t<span class="_ _11"></span><span class="ff1">)</span></div><div class="t m0 x11 hd y85 ff4 fs7 fc0 sc0 ls0 ws0">∫</div><div class="t m0 x12 h2 y7f ff1 fs0 fc0 sc0 ls1 ws31"> <span class="_ _12"></span> (1.1.1) </div><div class="t m0 x3 h2 y86 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 y87 ff1 fs0 fc0 sc0 ls0 ws1e">This can be considered to be only freque<span class="ls3 wsc">ncy representation of signal and this method </span></div><div class="t m0 x3 h2 y88 ff1 fs0 fc0 sc0 ls5 ws6">can be applied only to stationary signal. The time and frequency can be obtained by </div><div class="t m0 x3 h2 y89 ff1 fs0 fc0 sc0 ls5 ws6">cutting off only a well-localized slice (w<span class="ls7 ws21">indow) of signal and then take its Fourier </span></div><div class="t m0 x3 h2 y8a ff1 fs0 fc0 sc0 ls9 ws0">transform: </div><div class="t m0 x3 h2 y8b ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x7 he y8c ff1 fs8 fc0 sc0 ls0 ws0">(<span class="_ _13"></span><span class="ff3">T</span></div><div class="t m0 x13 hf y8d ff3 fs9 fc0 sc0 ls0 ws0">win</div><div class="t m0 x14 he y8c ff3 fs8 fc0 sc0 ls0 ws0">f<span class="_ _10"> </span><span class="ff1">)(</span></div><div class="c x15 y8e w3 h10"><div class="t m3 x0 h11 y8f ff4 fsa fc0 sc0 ls0 ws0">ω</div></div><div class="t m0 x16 he y8c ff1 fs8 fc0 sc0 ls0 ws0">,<span class="_ _14"></span><span class="ff3">t<span class="_ _11"></span></span>)<span class="_ _10"> </span><span class="ff4">=<span class="_ _15"> </span><span class="ff3">dsf<span class="_ _10"> </span></span></span>(<span class="_ _f"></span><span class="ff3">s<span class="_ _11"></span></span>)<span class="_ _f"></span><span class="ff3">g</span>(<span class="_ _11"></span><span class="ff3">s</span></div><div class="c x17 y8e w4 h10"><div class="t m0 x0 h12 y8f ff4 fs8 fc0 sc0 ls0 ws0">−</div></div><div class="t m0 x18 he y8c ff3 fs8 fc0 sc0 ls0 ws0">t<span class="_ _11"></span><span class="ff1">)</span>e</div><div class="c x19 y90 w5 h13"><div class="t m0 x0 h14 y91 ff4 fs9 fc0 sc0 ls0 ws0">−</div></div><div class="t m0 x1a hf y8d ff3 fs9 fc0 sc0 ls0 ws0">i</div><div class="c x1b y90 w6 h13"><div class="t m1 x0 h15 y91 ff4 fsb fc0 sc0 ls0 ws0">ω</div></div><div class="t m0 x1c hf y8d ff3 fs9 fc0 sc0 ls0 ws0">s</div><div class="c x1d y92 w7 h16"><div class="t m0 x0 h17 y93 ff4 fsc fc0 sc0 ls0 ws0">∫</div></div><div class="t m0 x1e h2 y8c ff1 fs0 fc0 sc0 ls7 ws32"> <span class="_ _16"></span> (1.1.2) <span class="_ _17"></span> </div><div class="t m0 x3 h2 y94 ff1 fs0 fc0 sc0 lsa ws0">or </div><div class="t m0 x1 h2 y95 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x1 h18 y96 ff5 fsd fc0 sc0 ls0 ws0"> </div><div class="t m0 x7 h19 y97 ff1 fsd fc0 sc0 ls0 ws0">(<span class="_ _13"></span><span class="ff3">T</span></div><div class="t m0 x1f h1a y98 ff3 fse fc0 sc0 ls0 ws0">m<span class="_ _f"></span><span class="ff1">,<span class="_ _f"></span></span>n</div><div class="t m0 x13 h1b y99 ff3 fse fc0 sc0 ls0 ws0">win</div><div class="t m0 x20 h19 y9a ff1 fsd fc0 sc0 ls0 ws0">)(<span class="_ _18"> </span><span class="ff3">f<span class="_ _10"> </span></span>)</div><div class="c x21 y9b w4 h1c"><div class="t m0 x0 h1d y9c ff4 fsd fc0 sc0 ls0 ws0">=</div></div><div class="t m0 x22 h19 y9a ff3 fsd fc0 sc0 ls0 ws0">dsf<span class="_ _18"> </span><span class="ff1">(<span class="_ _11"></span></span>s<span class="_ _f"></span><span class="ff1">)<span class="_ _11"></span></span>g<span class="ff1">(<span class="_ _11"></span></span>s</div><div class="c x23 y9b w4 h1c"><div class="t m0 x0 h1d y9c ff4 fsd fc0 sc0 ls0 ws0">−</div></div><div class="t m0 x24 h1e y9a ff3 fsd fc0 sc0 ls0 ws0">nt</div><div class="t m0 x25 h1f y98 ff5 fse fc0 sc0 ls0 ws0">o</div><div class="t m0 x12 h19 y9a ff1 fsd fc0 sc0 ls0 ws0">)<span class="ff3">e</span></div><div class="c x26 y9d w5 h13"><div class="t m0 x0 h20 y91 ff4 fse fc0 sc0 ls0 ws0">−</div></div><div class="t m0 x27 h1b y9e ff3 fse fc0 sc0 ls0 ws0">im</div><div class="c x1a y9d w6 h13"><div class="t m4 x0 h21 y91 ff4 fsf fc0 sc0 ls0 ws0">ω</div></div><div class="t m0 x1c h22 y9f ff5 fs10 fc0 sc0 ls0 ws0">o</div><div class="t m0 x28 h1b y9e ff3 fse fc0 sc0 ls0 ws0">s</div><div class="c x29 ya0 w8 h23"><div class="t m0 x0 h24 ya1 ff4 fs11 fc0 sc0 ls0 ws0">∫</div></div><div class="t m0 x2a h2 y9a ff1 fs0 fc0 sc0 ls4 ws33"> <span class="_ _12"></span> (1.1.3) <span class="_ _17"></span> <span class="_ _17"></span> <span class="_ _17"></span> </div><div class="t m0 x3 h2 ya2 ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h2 ya3 ff1 fs0 fc0 sc0 ls0 wsb">(1.1.2) is the windowed Fourier transform ,w<span class="ls4 ws5">hich is a standard technique for time </span></div><div class="t m0 x3 h2 ya4 ff1 fs0 fc0 sc0 ls4 ws5">frequency localization. Formula (1.1.2) is obt<span class="ls7 wsa">ained from<span class="_ _0"></span> (1.1.1) by replacing discrete </span></div><div class="t m0 x3 h2 ya5 ff1 fs0 fc0 sc0 lsa wsf">value (<span class="ff3 ls0 ws0">t</span><span class="ls20 ws19"> into <span class="ff3 ls0 ws0">nt</span><span class="ls9 ws1e"> ). </span></span></div><div class="t m0 x3 h2 ya6 ff1 fs0 fc0 sc0 ls5 ws6">By replacing values: </div><div class="t m0 x2b h25 ya7 ff5 fs12 fc0 sc0 ls0 ws0">o<span class="_ _19"></span>o</div><div class="c xf ya8 w9 h26"><div class="t m5 x0 h27 ya9 ff4 fs13 fc0 sc0 ls0 ws0">ω</div></div><div class="c x2c ya8 w9 h26"><div class="t m5 x0 h27 ya9 ff4 fs13 fc0 sc0 ls0 ws0">ω</div></div><div class="t m0 x2d h2 yaa ff3 fs14 fc0 sc0 ls0 ws0">m<span class="_ _1a"></span>nt<span class="_ _1b"></span>t<span class="_ _1c"> </span><span class="ff4">=<span class="_ _1d"></span>=<span class="_ _1e"> </span><span class="ff1">,<span class="_ _1f"> </span><span class="fs0 ls5 ws6"> equations’ (1.1.3) can be obtained from (1.1.2). </span></span></span></div><div class="t m0 x3 h2 yab ff1 fs0 fc0 sc0 ls1 wsb">The windowed Fourier transform calls also<span class="ls7 ws17"> Short Fast Fourie<span class="_ _0"></span><span class="ls2 ws34">r Transform (SFFT). </span></span></div><div class="t m0 x3 h2 yac ff1 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 yad ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 yae ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h3 yaf ff2 fs0 fc0 sc0 lsb ws22">1.2 Wavelet transform </div><div class="t m0 x3 h2 yb0 ff1 fs0 fc0 sc0 ls0 ws0"> </div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>