CH6 - Convolution.rar

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DSP Guide to DSP Chapter 3
CH6 - Convolution.rar
  • CH6 - Convolution.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/625725b6bd8c6f2306b602d6/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/625725b6bd8c6f2306b602d6/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">107</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">6</div><div class="t m0 x4 h5 y4 ff2 fs3 fc0 sc0 ls3 ws1">Convolution </div><div class="t m0 x5 h6 y5 ff1 fs4 fc0 sc0 ls4 ws2">Convolution is a mathematical way of combining two signals to form a third signal. It is the</div><div class="t m0 x5 h6 y6 ff1 fs4 fc0 sc0 ls5 ws3">single most important technique in Digital Signal Processing. Using the strategy of impulse</div><div class="t m0 x5 h6 y7 ff1 fs4 fc0 sc0 ls6 ws4">decomposition, systems are described by a signal called the <span class="ff3 ls7 ws5">impulse response</span><span class="ls8 ws6">. Convolution is</span></div><div class="t m0 x5 h6 y8 ff1 fs4 fc0 sc0 ls9 ws7">important because it relates the three signals of interest: the input signal, the output signal, and</div><div class="t m0 x5 h6 y9 ff1 fs4 fc0 sc0 ls8 ws8">the impulse response. This chapter presents convolution from two different viewpoints, called</div><div class="t m0 x5 h6 ya ff1 fs4 fc0 sc0 lsa ws9">the input side algorithm and the output side algorithm. Convolution provides the mathematical</div><div class="t m0 x5 h6 yb ff1 fs4 fc0 sc0 lsb wsa">framework for DSP; there is nothing more important in this book. </div><div class="t m0 x5 h7 yc ff2 fs5 fc0 sc0 lsc wsb">The Delta Function and Impulse Response</div><div class="t m0 x6 h8 yd ff1 fs6 fc0 sc0 lsd wsc">The previous chapter describes how a signal can be decomposed into a group</div><div class="t m0 x6 h9 ye ff1 fs6 fc0 sc0 lse wsd">of components called <span class="ff4 lsf ws0">impulses</span><span class="ls10 wse">. An impulse is a signal composed of all zeros,</span></div><div class="t m0 x6 h8 yf ff1 fs6 fc0 sc0 ls11 wsf">except a single nonzero point. In effect, impulse decomposition provides a way</div><div class="t m0 x6 h8 y10 ff1 fs6 fc0 sc0 ls12 ws10">to analyze signals one sample at a time. The previous chapter also presented</div><div class="t m0 x6 h8 y11 ff1 fs6 fc0 sc0 ls13 ws11">the fundamental concept of DSP: the input signal is decomposed into simple</div><div class="t m0 x6 h8 y12 ff1 fs6 fc0 sc0 ls14 ws12">additive components, each of these components is passed through a linear</div><div class="t m0 x6 h8 y13 ff1 fs6 fc0 sc0 ls15 ws13">system, and the resulting output components are synthesized (added). The</div><div class="t m0 x6 h8 y14 ff1 fs6 fc0 sc0 ls16 ws14">signal resulting from this divide-and-conquer procedure is identical to that</div><div class="t m0 x6 h8 y15 ff1 fs6 fc0 sc0 ls17 ws15">obtained by directly passing the original signal through the system. While</div><div class="t m0 x6 h8 y16 ff1 fs6 fc0 sc0 ls18 ws16">many different decompositions are possible, two form the backbone of signal</div><div class="t m0 x6 h8 y17 ff1 fs6 fc0 sc0 ls19 ws17">processing: impulse decomposition and Fourier decomposition. When impulse</div><div class="t m0 x6 h8 y18 ff1 fs6 fc0 sc0 ls1a ws18">decomposition is used, the procedure can be described by a mathematical</div><div class="t m0 x6 h9 y19 ff1 fs6 fc0 sc0 ls1b ws19">operation called <span class="ff4 ls1c ws0">convolution</span><span class="ls1d ws1a">. In this chapter (and most of the following ones)</span></div><div class="t m0 x6 h8 y1a ff1 fs6 fc0 sc0 ls1e ws1b">we will only be dealing with <span class="ff3 ls1f ws0">discrete</span><span class="ls20 ws1c"> signals. Convolution also applies to</span></div><div class="t m0 x6 h8 y1b ff3 fs6 fc0 sc0 ls21 ws0">continuous<span class="ff1 ls22 ws1d"> signals, but the mathematics is more complicated. We will look at</span></div><div class="t m0 x6 h8 y1c ff1 fs6 fc0 sc0 ls23 ws1e">how continious signals are processed in Chapter 13. </div><div class="t m0 x6 h9 y1d ff1 fs6 fc0 sc0 ls24 ws1f">Figure 6-1 defines two important terms used in DSP. The first is the <span class="ff4 ls25 ws0">delta</span></div><div class="t m0 x6 h9 y1e ff4 fs6 fc0 sc0 ls26 ws0">function<span class="ff1 ls27 ws20">, symbolized by the Greek letter delta, <span class="_ _0"> </span><span class="ls28 ws21">. The delta function is</span></span></div><div class="c x7 y1f w2 ha"><div class="t m0 x8 hb y20 ff5 fs0 fc0 sc0 ls29 ws0">*<span class="_ _1"></span>*</div></div><div class="t m0 x9 hc y21 ff4 fs0 fc0 sc0 ls2a ws0">[<span class="ff6 ls2b">n</span>]</div><div class="t m0 x6 h8 y22 ff1 fs6 fc0 sc0 ls2c ws22">a <span class="ff3 ls2d ws0">normalized</span><span class="ls2e ws23"> impulse, that is, sample number zero has a value of one, while</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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