CH5 - Linear Systems.rar

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DSP Guide to DSP Chapter 5
CH5 - Linear Systems.rar
  • CH5 - Linear Systems.pdf
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内容介绍
<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/625b4c68be9ad24cfa0972a7/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/625b4c68be9ad24cfa0972a7/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">87</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls1 ws0">CHAPTER</div><div class="t m0 x3 h4 y3 ff1 fs2 fc0 sc0 ls2 ws0">5</div><div class="t m0 x4 h5 y4 ff2 fs3 fc0 sc0 ls3 ws1">Linear Systems </div><div class="t m0 x5 h6 y5 ff1 fs4 fc0 sc0 ls4 ws2">Most DSP techniques are based on a divide-and-conquer strategy called <span class="ff3 ls5 ws0">superposition</span><span class="ls6 ws3">. The</span></div><div class="t m0 x5 h6 y6 ff1 fs4 fc0 sc0 ls7 ws4">signal being processed is broken into simple components, each component is processed</div><div class="t m0 x5 h6 y7 ff1 fs4 fc0 sc0 ls8 ws5">individually, and the results reunited. This approach has the tremendous power of breaking a</div><div class="t m0 x5 h6 y8 ff1 fs4 fc0 sc0 ls9 ws6">single complicated problem into many easy ones. Superposition can only be used with <span class="ff3 lsa ws0">linear</span></div><div class="t m0 x5 h6 y9 ff3 fs4 fc0 sc0 lsb ws0">systems<span class="ff1 lsc ws7">, a term meaning that certain mathematical rules apply. Fortunately, most of the</span></div><div class="t m0 x5 h6 ya ff1 fs4 fc0 sc0 lsd ws8">applications encountered in science and engineering fall into this category. This chapter presents</div><div class="t m0 x5 h6 yb ff1 fs4 fc0 sc0 lse ws9">the foundation of DSP: what it means for a system to be linear, various ways for breaking signals</div><div class="t m0 x5 h6 yc ff1 fs4 fc0 sc0 lsf wsa">into simpler components, and how superposition provides a variety of signal processing</div><div class="t m0 x5 h6 yd ff1 fs4 fc0 sc0 ls10 ws0">techniques.</div><div class="t m0 x5 h7 ye ff2 fs5 fc0 sc0 ls11 wsb">Signals and Systems</div><div class="t m0 x6 h8 yf ff1 fs6 fc0 sc0 ls12 wsc">A <span class="ff4 ls13 ws0">signal</span><span class="ls14 wsd"> is a description of how one parameter varies with another parameter.</span></div><div class="t m0 x6 h9 y10 ff1 fs6 fc0 sc0 ls15 wse">For instance, voltage changing over time in an electronic circuit, or brightness</div><div class="t m0 x6 h8 y11 ff1 fs6 fc0 sc0 ls16 wsf">varying with distance in an image. A <span class="ff4 ls17 ws0">system</span><span class="ls18 ws10"> is any process that produces an</span></div><div class="t m0 x6 h9 y12 ff3 fs6 fc0 sc0 ls19 ws11">output signal<span class="ff1 ls1a ws12"> in response to an </span><span class="ls1b ws13">input signal<span class="ff1 ls1c ws14">. This is illustrated by the block</span></span></div><div class="t m0 x6 h9 y13 ff1 fs6 fc0 sc0 ls1d ws15">diagram in Fig. 5-1. Continuous systems input and output continuous signals,</div><div class="t m0 x6 h9 y14 ff1 fs6 fc0 sc0 ls1e ws16">such as in analog electronics. Discrete systems input and output discrete</div><div class="t m0 x6 h9 y15 ff1 fs6 fc0 sc0 ls1f ws17">signals, such as computer programs that manipulate the values stored in arrays.</div><div class="t m0 x6 h9 y16 ff1 fs6 fc0 sc0 ls9 ws18">Several rules are used for naming signals. These aren't always followed in</div><div class="t m0 x6 h9 y17 ff1 fs6 fc0 sc0 ls20 ws19">DSP, but they are very common and you should memorize them. The</div><div class="t m0 x6 h9 y18 ff1 fs6 fc0 sc0 ls21 ws1a">mathematics is difficult enough without a clear notation. First, <span class="ff3 ls22 ws0">continuous</span></div><div class="t m0 x6 h9 y19 ff1 fs6 fc0 sc0 ls23 ws1b">signals use parentheses, such as: <span class="_ _0"> </span><span class="ls24 ws1c"> and <span class="_ _0"> </span><span class="ls25 ws1d">, while <span class="ff3 ls26 ws0">discrete</span><span class="ls27 ws1e"> signals use<span class="_ _1"></span><span class="ff3 fs0 ls28 ws0">x<span class="ff1 ls29">(</span><span class="ls2a">t<span class="ff1 ls29">)<span class="_ _2"> </span></span></span>y<span class="ff1 ls29">(</span><span class="ls2a">t<span class="ff1 ls29">)</span></span></span></span></span></span></div><div class="t m0 x6 h9 y1a ff1 fs6 fc0 sc0 ls2b ws1f">brackets, as in: <span class="_ _3"> </span><span class="ls24 ws20"> and <span class="_ _3"> </span><span class="ls2c ws21">. Second, signals use lower case letters. Upper<span class="_ _4"></span><span class="ff3 fs0 ls28 ws0">x<span class="ff1 ls29">[</span><span class="ls0">n<span class="ff1 ls29">]<span class="_ _5"> </span></span></span>y<span class="ff1 ls29">[</span><span class="ls0">n<span class="ff1 ls29">]</span></span></span></span></span></div><div class="t m0 x6 h9 y1b ff1 fs6 fc0 sc0 ls2d ws22">case letters are reserved for the frequency domain, discussed in later chapters.</div><div class="t m0 x6 h9 y1c ff1 fs6 fc0 sc0 ls2e ws23">Third, the name given to a signal is usually descriptive of the parameters it</div><div class="t m0 x6 h9 y1d ff1 fs6 fc0 sc0 ls2f ws24">represents. For example, a <span class="ff3 ls30 ws0">voltage</span><span class="ls31 ws25"> depending on <span class="ff3 ls32 ws0">time</span><span class="ls33 ws26"> might be called: <span class="_ _0"> </span><span class="ls34 ws27">, or<span class="_ _6"></span><span class="ff3 fs0 ls28 ws0">v<span class="ff1 ls29">(</span><span class="ls2a">t<span class="ff1 ls29">)</span></span></span></span></span></span></div><div class="t m0 x6 h9 y1e ff1 fs6 fc0 sc0 ls35 ws28">a stock market <span class="ff3 ls36 ws0">price</span><span class="ls37 ws29"> measured each <span class="ff3 ls38 ws0">day</span><span class="ls39 ws2a"> could be: <span class="_ _7"> </span><span class="ls3a ws0">.<span class="_ _8"></span><span class="ff3 fs0 ls0">p<span class="ff1 ls29">[</span>d<span class="ff1 ls29">]</span></span></span></span></span></div></div><div class="pi" data-data='{"ctm":[1.839080,0.000000,0.000000,1.839080,0.000000,0.000000]}'></div></div> </body> </html>
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