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<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/624ef22a74bc5c01051c4057/bg1.jpg"><div class="c x1 y1 w2 h2"><div class="t m0 x2 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">Time-Frequency</div><div class="t m0 x3 h3 y3 ff1 fs0 fc0 sc0 ls0 ws0">Toolbox</div><div class="t m0 x4 h4 y4 ff1 fs1 fc0 sc0 ls0 ws0">For Use with MATLAB</div><div class="t m0 x5 h5 y5 ff2 fs2 fc0 sc0 ls0 ws0">François Auger *</div><div class="t m0 x5 h5 y6 ff2 fs2 fc0 sc0 ls0 ws0">Patrick Flandrin *</div><div class="t m0 x5 h5 y7 ff2 fs2 fc0 sc0 ls0 ws0">Paulo Gonçalvès °</div><div class="t m0 x5 h5 y8 ff2 fs2 fc0 sc0 ls0 ws0">Olivier Lemoine *</div><div class="t m0 x5 h5 y9 ff2 fs2 fc0 sc0 ls0 ws0">* CNRS (France)</div><div class="t m0 x5 h5 ya ff2 fs2 fc0 sc0 ls0 ws0">° Rice University (USA)</div><div class="t m0 x6 h5 yb ff2 fs2 fc0 sc0 ls0 ws0"> 1995-1996</div></div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>
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<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/624ef22a74bc5c01051c4057/bg2.jpg"><div class="t m1 x7 h6 yc ff3 fs3 fc0 sc0 ls0 ws0">2</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/624ef22a74bc5c01051c4057/bg3.jpg"><div class="t m1 x8 h6 yc ff3 fs3 fc0 sc0 ls0 ws0">3</div><div class="t m1 x9 h6 yd ff3 fs3 fc0 sc0 ls0 ws0">Cop<span class="_ _0"></span>yrigh<span class="_ _0"></span>t<span class="_ _1"> </span>(C)<span class="_ _1"> </span>1996<span class="_ _1"> </span>CNRS<span class="_ _1"> </span>(F<span class="_ _2"></span>rance)<span class="_ _1"> </span>and<span class="_ _1"> </span>Rice<span class="_ _1"> </span>Universit<span class="_ _3"></span>y<span class="_ _1"> </span>(USA).</div><div class="t m1 xa h6 ye ff3 fs3 fc0 sc0 ls0 ws0">P<span class="_ _3"></span>ermission<span class="_ _4"> </span>is<span class="_ _4"> </span>gran<span class="_ _3"></span>ted<span class="_ _4"> </span>to<span class="_ _5"> </span>cop<span class="_ _0"></span>y<span class="_ _2"></span>,<span class="_ _4"> </span>distribute<span class="_ _5"> </span>and/or<span class="_ _4"> </span>modify<span class="_ _4"> </span>this<span class="_ _5"> </span>do<span class="_ _6"></span>cumen<span class="_ _0"></span>t<span class="_ _5"> </span>under</div><div class="t m1 xa h6 yf ff3 fs3 fc0 sc0 ls0 ws0">the<span class="_ _1"> </span>terms<span class="_ _1"> </span>of<span class="_ _4"> </span>the<span class="_ _1"> </span>GNU<span class="_ _1"> </span>F<span class="_ _2"></span>ree<span class="_ _1"> </span>Do<span class="_ _6"></span>cumen<span class="_ _3"></span>tation<span class="_ _1"> </span>License,<span class="_ _1"> </span>V<span class="_ _2"></span>ersion<span class="_ _4"> </span>1.2<span class="_ _1"> </span>or<span class="_ _1"> </span>an<span class="_ _0"></span>y<span class="_ _1"> </span>later</div><div class="t m1 xa h6 y10 ff3 fs3 fc0 sc0 ls0 ws0">v<span class="_ _3"></span>ersion<span class="_ _7"> </span>published<span class="_ _7"> </span>b<span class="_ _3"></span>y<span class="_ _7"> </span>the<span class="_ _8"> </span>F<span class="_ _2"></span>ree<span class="_ _8"> </span>Softw<span class="_ _3"></span>are<span class="_ _7"> </span>F<span class="_ _9"></span>oundation;<span class="_ _7"> </span>with<span class="_ _7"> </span>no<span class="_ _8"> </span>Inv<span class="_ _2"></span>arian<span class="_ _0"></span>t<span class="_ _8"> </span>Sec-</div><div class="t m1 xa h6 y11 ff3 fs3 fc0 sc0 ls0 ws0">tions,<span class="_ _4"> </span>no<span class="_ _4"> </span>F<span class="_ _2"></span>ron<span class="_ _0"></span>t-Co<span class="_ _3"></span>ver<span class="_ _4"> </span>T<span class="_ _9"></span>exts,<span class="_ _4"> </span>and<span class="_ _4"> </span>no<span class="_ _4"> </span>Back-Co<span class="_ _3"></span>ver<span class="_ _4"> </span>T<span class="_ _9"></span>exts.<span class="_ _7"> </span>A<span class="_ _4"> </span>copy<span class="_ _4"> </span>of<span class="_ _4"> </span>the<span class="_ _4"> </span>license</div><div class="t m1 xa h6 y12 ff3 fs3 fc0 sc0 ls0 ws0">is<span class="_ _1"> </span>included<span class="_ _1"> </span>in<span class="_ _1"> </span>the<span class="_ _1"> </span>section<span class="_ _1"> </span>entitled<span class="_ _1"> </span>”GNU<span class="_ _1"> </span>F<span class="_ _9"></span>ree<span class="_ _1"> </span>Do<span class="_ _6"></span>cumen<span class="_ _3"></span>tation<span class="_ _1"> </span>License”.</div><div class="t m1 x9 h6 y13 ff3 fs3 fc0 sc0 ls0 ws0">The<span class="_ _1"> </span>Time-F<span class="_ _9"></span>requency<span class="_ _1"> </span>T<span class="_ _2"></span>o<span class="_ _6"></span>olbox<span class="_ _4"> </span>has<span class="_ _1"> </span>b<span class="_ _6"></span>een<span class="_ _1"> </span>mainly<span class="_ _1"> </span>dev<span class="_ _3"></span>elop<span class="_ _6"></span>ed<span class="_ _1"> </span>under<span class="_ _1"> </span>the<span class="_ _1"> </span>aus-</div><div class="t m1 xa h6 y14 ff3 fs3 fc0 sc0 ls0 ws0">pices<span class="_ _4"> </span>of<span class="_ _1"> </span>the<span class="_ _4"> </span>F<span class="_ _2"></span>rench<span class="_ _4"> </span>CNRS<span class="_ _4"> </span>(<span class="ff4">Centr<span class="_ _3"></span>e<span class="_ _8"> </span>National<span class="_ _1"> </span>de<span class="_ _1"> </span>la<span class="_ _1"> </span>R<span class="_ _3"></span>e<span class="_ _3"></span>cher<span class="_ _3"></span>che<span class="_ _1"> </span>Scientifique<span class="ff3">).<span class="_ _a"> </span>It</span></span></div><div class="t m1 xa h6 y15 ff3 fs3 fc0 sc0 ls0 ws0">results<span class="_ _5"> </span>from<span class="_ _5"> </span>a<span class="_ _b"> </span>researc<span class="_ _0"></span>h<span class="_ _b"> </span>effort<span class="_ _5"> </span>conducted<span class="_ _5"> </span>within<span class="_ _b"> </span>its<span class="_ _5"> </span>Group<span class="_ _6"></span>emen<span class="_ _3"></span>ts<span class="_ _5"> </span>de<span class="_ _5"> </span>Rec<span class="_ _3"></span>herche</div><div class="t m1 xa h6 y16 ff3 fs3 fc0 sc0 ls0 ws0">”T<span class="_ _9"></span>raitement<span class="_ _8"> </span>du<span class="_ _8"> </span>Signal<span class="_ _1"> </span>et<span class="_ _8"> </span>Images”<span class="_ _8"> </span>(O.<span class="_ _8"> </span>Macchi)<span class="_ _c"> </span>and<span class="_ _c"> </span>”Information,<span class="_ _7"> </span>Signal<span class="_ _c"> </span>et</div><div class="t m1 xa h6 y17 ff3 fs3 fc0 sc0 ls0 ws0">Images”<span class="_ _4"> </span>(J.-M.<span class="_ _4"> </span>Chassery).<span class="_ _a"> </span>P<span class="_ _3"></span>arts<span class="_ _1"> </span>of<span class="_ _4"> </span>the<span class="_ _4"> </span>T<span class="_ _9"></span>o<span class="_ _6"></span>olb<span class="_ _6"></span>o<span class="_ _3"></span>x<span class="_ _4"> </span>hav<span class="_ _3"></span>e<span class="_ _4"> </span>also<span class="_ _1"> </span>been<span class="_ _1"> </span>dev<span class="_ _3"></span>elop<span class="_ _6"></span>ed<span class="_ _4"> </span>at</div><div class="t m1 xa h6 y18 ff3 fs3 fc0 sc0 ls0 ws0">Rice<span class="_ _1"> </span>Univ<span class="_ _0"></span>ersit<span class="_ _0"></span>y<span class="_ _9"></span>,<span class="_ _c"> </span>when<span class="_ _1"> </span>one<span class="_ _1"> </span>of<span class="_ _1"> </span>the<span class="_ _c"> </span>authors<span class="_ _1"> </span>(PG)<span class="_ _1"> </span>was<span class="_ _1"> </span>visiting<span class="_ _1"> </span>the<span class="_ _1"> </span>Department</div><div class="t m1 xa h6 y19 ff3 fs3 fc0 sc0 ls0 ws0">of<span class="_ _1"> </span>Electrical<span class="_ _c"> </span>and<span class="_ _c"> </span>Computer<span class="_ _1"> </span>Engineering,<span class="_ _c"> </span>supp<span class="_ _6"></span>orted<span class="_ _1"> </span>by<span class="_ _1"> </span>NSF.<span class="_ _1"> </span>Supp<span class="_ _6"></span>orting<span class="_ _c"> </span>in-</div><div class="t m1 xa h6 y1a ff3 fs3 fc0 sc0 ls0 ws0">stitutions<span class="_ _8"> </span>are<span class="_ _7"> </span>gratefully<span class="_ _8"> </span>ackno<span class="_ _3"></span>wledged,<span class="_ _7"> </span>as<span class="_ _8"> </span>well<span class="_ _8"> </span>as<span class="_ _7"> </span>M.<span class="_ _8"> </span>Guglielmi,<span class="_ _7"> </span>M.<span class="_ _8"> </span>Na<span class="_ _d"></span>jim,</div><div class="t m1 xa h6 y1b ff3 fs3 fc0 sc0 ls0 ws0">R.<span class="_ _8"> </span>Settineri,<span class="_ _7"> </span>R.G.<span class="_ _8"> </span>Baraniuk,<span class="_ _7"> </span>M.<span class="_ _7"> </span>Chausse,<span class="_ _8"> </span>D.<span class="_ _7"> </span>Roche,<span class="_ _8"> </span>E.<span class="_ _7"> </span>Chassande-Mottin,</div><div class="t m1 xa h6 y1c ff3 fs3 fc0 sc0 ls0 ws0">O.<span class="_ _1"> </span>Mic<span class="_ _3"></span>hel<span class="_ _1"> </span>and<span class="_ _1"> </span>P<span class="_ _9"></span>.<span class="_ _1"> </span>Abry<span class="_ _4"> </span>for<span class="_ _1"> </span>their<span class="_ _1"> </span>help<span class="_ _1"> </span>at<span class="_ _4"> </span>different<span class="_ _4"> </span>phases<span class="_ _1"> </span>of<span class="_ _1"> </span>the<span class="_ _4"> </span>developmen<span class="_ _3"></span>t.</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/624ef22a74bc5c01051c4057/bg4.jpg"><div class="t m1 x7 h6 yc ff3 fs3 fc0 sc0 ls0 ws0">4</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/624ef22a74bc5c01051c4057/bg5.jpg"><div class="t m1 xa h7 y1d ff5 fs4 fc0 sc0 ls0 ws0">Con<span class="_ _2"></span>ten<span class="_ _2"></span>ts</div><div class="t m1 xa h8 y1e ff5 fs3 fc0 sc0 ls0 ws0">1<span class="_ _e"> </span>In<span class="_ _3"></span>tro<span class="_ _6"></span>duction<span class="_ _f"> </span>9</div><div class="t m1 x9 h6 y1f ff3 fs3 fc0 sc0 ls0 ws0">1.1<span class="_ _10"> </span>Presen<span class="_ _0"></span>tation<span class="_ _7"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _13"> </span>9</div><div class="t m1 x9 h6 y20 ff3 fs3 fc0 sc0 ls0 ws0">1.2<span class="_ _10"> </span>Bac<span class="_ _0"></span>kground,<span class="_ _1"> </span>system<span class="_ _1"> </span>requiremen<span class="_ _0"></span>ts<span class="_ _1"> </span>and</div><div class="t m1 xb h6 y21 ff3 fs3 fc0 sc0 ls0 ws0">installation<span class="_ _10"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _e"> </span>10</div><div class="t m1 x9 h6 y22 ff3 fs3 fc0 sc0 ls0 ws0">1.3<span class="_ _10"> </span>In<span class="_ _0"></span>tro<span class="_ _6"></span>ductory<span class="_ _1"> </span>examples<span class="_ _14"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _e"> </span>10</div><div class="t m1 xb h6 y23 ff3 fs3 fc0 sc0 ls0 ws0">1.3.1<span class="_ _15"> </span>Example<span class="_ _1"> </span>1<span class="_ _7"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _e"> </span>10</div><div class="t m1 xb h6 y24 ff3 fs3 fc0 sc0 ls0 ws0">1.3.2<span class="_ _15"> </span>Example<span class="_ _1"> </span>2<span class="_ _7"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _e"> </span>13</div><div class="t m1 xb h6 y25 ff3 fs3 fc0 sc0 ls0 ws0">1.3.3<span class="_ _15"> </span>Example<span class="_ _1"> </span>3<span class="_ _7"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _e"> </span>14</div><div class="t m1 xa h8 y26 ff5 fs3 fc0 sc0 ls0 ws0">2<span class="_ _e"> </span>Non<span class="_ _8"> </span>stationary<span class="_ _8"> </span>signals<span class="_ _16"> </span>19</div><div class="t m1 x9 h6 y27 ff3 fs3 fc0 sc0 ls0 ws0">2.1<span class="_ _10"> </span>Time<span class="_ _1"> </span>represen<span class="_ _0"></span>tation<span class="_ _1"> </span>and<span class="_ _1"> </span>frequency<span class="_ _1"> </span>representation<span class="_ _17"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _e"> </span>19</div><div class="t m1 x9 h6 y28 ff3 fs3 fc0 sc0 ls0 ws0">2.2<span class="_ _10"> </span>Lo<span class="_ _6"></span>calization<span class="_ _1"> </span>and<span class="_ _1"> </span>the<span class="_ _1"> </span>Heisen<span class="_ _3"></span>b<span class="_ _6"></span>erg-Gab<span class="_ _6"></span>or</div><div class="t m1 xb h6 y29 ff3 fs3 fc0 sc0 ls0 ws0">principle<span class="_ _18"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _e"> </span>20</div><div class="t m1 xb h6 y2a ff3 fs3 fc0 sc0 ls0 ws0">2.2.1<span class="_ _15"> </span>Example<span class="_ _1"> </span>1<span class="_ _7"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _e"> </span>20</div><div class="t m1 xb h6 y2b ff3 fs3 fc0 sc0 ls0 ws0">2.2.2<span class="_ _15"> </span>Example<span class="_ _1"> </span>2<span class="_ _7"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _e"> </span>21</div><div class="t m1 x9 h6 y2c ff3 fs3 fc0 sc0 ls0 ws0">2.3<span class="_ _10"> </span>Instan<span class="_ _0"></span>taneous<span class="_ _1"> </span>frequency<span class="_ _19"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _e"> </span>22</div><div class="t m1 x9 h6 y2d ff3 fs3 fc0 sc0 ls0 ws0">2.4<span class="_ _10"> </span>Group<span class="_ _1"> </span>dela<span class="_ _0"></span>y<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _e"> </span>24</div><div class="t m1 x9 h6 y2e ff3 fs3 fc0 sc0 ls0 ws0">2.5<span class="_ _10"> </span>Ab<span class="_ _6"></span>out<span class="_ _1"> </span>stationarit<span class="_ _3"></span>y<span class="_ _e"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _e"> </span>25</div><div class="t m1 x9 h6 y2f ff3 fs3 fc0 sc0 ls0 ws0">2.6<span class="_ _10"> </span>Ho<span class="_ _0"></span>w<span class="_ _1"> </span>to<span class="_ _1"> </span>syn<span class="_ _0"></span>thesize<span class="_ _1"> </span>a<span class="_ _1"> </span>mono-comp<span class="_ _6"></span>onen<span class="_ _3"></span>t<span class="_ _1"> </span>non-stationary<span class="_ _c"> </span>signal<span class="_ _4"> </span>.<span class="_ _11"> </span>.<span class="_ _e"> </span>26</div><div class="t m1 x9 h6 y30 ff3 fs3 fc0 sc0 ls0 ws0">2.7<span class="_ _10"> </span>What<span class="_ _1"> </span>ab<span class="_ _6"></span>out<span class="_ _1"> </span>m<span class="_ _3"></span>ulti-comp<span class="_ _6"></span>onen<span class="_ _0"></span>t<span class="_ _1"> </span>non-stationary<span class="_ _1"> </span>signals<span class="_ _1"> </span>?<span class="_ _10"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _e"> </span>29</div><div class="t m1 xa h8 y31 ff5 fs3 fc0 sc0 ls0 ws0">3<span class="_ _e"> </span>First<span class="_ _8"> </span>class<span class="_ _8"> </span>of<span class="_ _7"> </span>solutions<span class="_ _c"> </span>:<span class="_ _11"> </span>the<span class="_ _8"> </span>atomic<span class="_ _7"> </span>decompositions<span class="_ _1a"> </span>33</div><div class="t m1 x9 h6 y32 ff3 fs3 fc0 sc0 ls0 ws0">3.1<span class="_ _10"> </span>The<span class="_ _1"> </span>Short-Time<span class="_ _1"> </span>F<span class="_ _9"></span>ourier<span class="_ _c"> </span>T<span class="_ _9"></span>ransform<span class="_ _19"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _e"> </span>33</div><div class="t m1 xb h6 y33 ff3 fs3 fc0 sc0 ls0 ws0">3.1.1<span class="_ _15"> </span>Definition<span class="_ _14"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _1b"> </span>33</div><div class="t m1 xb h6 y34 ff3 fs3 fc0 sc0 ls0 ws0">3.1.2<span class="_ _15"> </span>An<span class="_ _1"> </span>example<span class="_ _17"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _1b"> </span>35</div><div class="t m1 xb h6 y35 ff3 fs3 fc0 sc0 ls0 ws0">3.1.3<span class="_ _15"> </span>Some<span class="_ _1"> </span>prop<span class="_ _6"></span>erties<span class="_ _7"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _1b"> </span>36</div><div class="t m1 xb h6 y36 ff3 fs3 fc0 sc0 ls0 ws0">3.1.4<span class="_ _15"> </span>Time-frequency<span class="_ _1"> </span>resolution<span class="_ _14"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _e"> </span>37</div><div class="t m1 x9 h6 y37 ff3 fs3 fc0 sc0 ls0 ws0">3.2<span class="_ _10"> </span>Time-scale<span class="_ _1"> </span>analysis<span class="_ _1"> </span>and<span class="_ _1"> </span>the<span class="_ _1"> </span>wa<span class="_ _3"></span>v<span class="_ _0"></span>elet<span class="_ _1"> </span>transform<span class="_ _17"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _1b"> </span>40</div><div class="t m1 xb h6 y38 ff3 fs3 fc0 sc0 ls0 ws0">3.2.1<span class="_ _15"> </span>Definitions<span class="_ _1"> </span>and<span class="_ _1"> </span>in<span class="_ _0"></span>terpretation<span class="_ _1c"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _e"> </span>41</div><div class="t m1 xb h6 y39 ff3 fs3 fc0 sc0 ls0 ws0">3.2.2<span class="_ _15"> </span>Prop<span class="_ _6"></span>erties<span class="_ _18"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _e"> </span>42</div><div class="t m1 x9 h6 y3a ff3 fs3 fc0 sc0 ls0 ws0">3.3<span class="_ _10"> </span>Sampling<span class="_ _1"> </span>considerations<span class="_ _1d"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _11"> </span>.<span class="_ _12"> </span>.<span class="_ _11"> </span>.<span class="_ _1b"> </span>43</div><div class="t m1 xc h6 y3b ff3 fs3 fc0 sc0 ls0 ws0">5</div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>