CH2 - Statistics, Probability and Noise.rar

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  • 2020-03-24 16:18
DSP Guide to DSP chapter 2
CH2 - Statistics, Probability and Noise.rar
  • CH2 - Statistics, Probability and Noise.pdf
<html xmlns=""> <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=""> <link rel="stylesheet" href=""> <link rel="stylesheet" href=""> <script src=""></script> <script src=""></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=""><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">11</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">2</div><div class="t m0 x4 h5 y4 ff2 fs3 fc0 sc0 ls3 ws1">Statistics, Probability and Noise</div><div class="t m0 x5 h6 y5 ff1 fs4 fc0 sc0 ls4 ws2">Statistics and probability are used in Digital Signal Processing to characterize signals and the</div><div class="t m0 x5 h6 y6 ff1 fs4 fc0 sc0 ls5 ws3">processes that generate them. For example, a primary use of DSP is to reduce interference, noise,</div><div class="t m0 x5 h6 y7 ff1 fs4 fc0 sc0 ls6 ws4">and other undesirable components in acquired data. These may be an inherent part of the signal</div><div class="t m0 x5 h6 y8 ff1 fs4 fc0 sc0 ls7 ws5">being measured, arise from imperfections in the data acquisition system, or be introduced as an</div><div class="t m0 x5 h6 y9 ff1 fs4 fc0 sc0 ls8 ws6">unavoidable byproduct of some DSP operation. Statistics and probability allow these disruptive</div><div class="t m0 x5 h6 ya ff1 fs4 fc0 sc0 ls9 ws7">features to be measured and classified, the first step in developing strategies to remove the</div><div class="t m0 x5 h6 yb ff1 fs4 fc0 sc0 lsa ws8">offending components. This chapter introduces the most important concepts in statistics and</div><div class="t m0 x5 h6 yc ff1 fs4 fc0 sc0 lsb ws9">probability, with emphasis on how they apply to acquired signals. </div><div class="t m0 x5 h7 yd ff2 fs5 fc0 sc0 lsc wsa">Signal and Graph Terminology</div><div class="t m0 x6 h8 ye ff1 fs6 fc0 sc0 lsd wsb">A <span class="ff3 lse ws0">signal</span><span class="lsf wsc"> is a description of how one parameter is related to another parameter.</span></div><div class="t m0 x6 h8 yf ff1 fs6 fc0 sc0 ls10 wsd">For example, the most common type of signal in analog electronics is a <span class="ff3 ls11 ws0">voltage</span></div><div class="t m0 x6 h8 y10 ff1 fs6 fc0 sc0 ls12 wse">that varies with <span class="ff3 ls13 ws0">time</span><span class="ls14 wsf">. Since both parameters can assume a continuous range</span></div><div class="t m0 x6 h9 y11 ff1 fs6 fc0 sc0 ls15 ws10">of values, we will call this a <span class="ff4 ls16 ws11">continuous signal</span><span class="ls17 ws12">. In comparison, passing this</span></div><div class="t m0 x6 h8 y12 ff1 fs6 fc0 sc0 ls18 ws13">signal through an analog-to-digital converter forces each of the two parameters</div><div class="t m0 x6 h8 y13 ff1 fs6 fc0 sc0 ls19 ws14">to be <span class="ff3 ls1a ws0">quantized</span><span class="ls1b ws15">. For instance, imagine the conversion being done with 12 bits</span></div><div class="t m0 x6 h8 y14 ff1 fs6 fc0 sc0 ls1c ws16">at a sampling rate of 1000 samples per second. The voltage is curtailed to 4096</div><div class="t m0 x6 h8 y15 ff1 fs6 fc0 sc0 ls1d ws0">(2</div><div class="t m0 x7 ha y16 ff1 fs7 fc0 sc0 ls1e ws0">12</div><div class="t m0 x8 h8 y15 ff1 fs6 fc0 sc0 ls1f ws17">) possible binary levels, and the time is only defined at one millisecond</div><div class="t m0 x6 h8 y17 ff1 fs6 fc0 sc0 ls20 ws18">increments. Signals formed from parameters that are quantized in this manner</div><div class="t m0 x6 h9 y18 ff1 fs6 fc0 sc0 ls21 ws19">are said to be <span class="ff4 ls22 ws1a">discrete signals</span><span class="ls23 ws1b"> or <span class="ff4 ls24 ws1c">digitized signals</span><span class="ls25 ws1d">. For the most part,</span></span></div><div class="t m0 x6 h8 y19 ff1 fs6 fc0 sc0 ls26 ws1e">continuous signals exist in nature, while discrete signals exist inside computers</div><div class="t m0 x6 h8 y1a ff1 fs6 fc0 sc0 ls27 ws1f">(although you can find exceptions to both cases). It is also possible to have</div><div class="t m0 x6 h8 y1b ff1 fs6 fc0 sc0 ls28 ws20">signals where one parameter is continuous and the other is discrete. Since</div><div class="t m0 x6 h8 y1c ff1 fs6 fc0 sc0 ls29 ws21">these mixed signals are quite uncommon, they do not have special names given</div><div class="t m0 x6 h8 y1d ff1 fs6 fc0 sc0 ls2a ws22">to them, and the nature of the two parameters must be explicitly stated.</div><div class="t m0 x6 h8 y1e ff1 fs6 fc0 sc0 ls2b ws23">Figure 2-1 shows two discrete signals, such as might be acquired with a</div><div class="t m0 x6 h9 y1f ff1 fs6 fc0 sc0 ls2c ws24">digital data acquisition system. The <span class="ff4 ls2d ws25">vertical axis</span><span class="ls2e ws26"> may represent voltage, light</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>