三角波傅里叶级数与有效值
2020-07-31 11:36
本范例演示了三角波的傅里叶级数展开及其有效值的计算。通过调整项数n和频率f等参数，可以观察有限项傅里叶级数如何逼近理想的三角波波形，并直观理解信号处理中的频域分析与有效值概念。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.573.0" app="classic" platform="offline" id="ECAAEAC4-AF37-4438-A52A-C7E2A4CA66F6" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1904" height="1042" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.19012605042016806" orientation="1" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 51 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 | 1009 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="384" window="100,100,700,550" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1534" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="362" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="300" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="300" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="900" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1534" height="989"/>
<coordSystem xZero="205.7486602255936" yZero="656.3764275736089" scale="62.355708804056206" yscale="62.35570880405597"/>
<evSettings axes="true" grid="true" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<algebraView>
<mode val="3"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="3" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="三角波傅立葉級數&有效值" author="" date="">
<element type="numeric" label="n">
<value val="1"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="20" absoluteScreenLocation="true" width="200" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Sum">
<input a0="((-1)^(k - 1) * sin((((2 * k) - 1) * x)) / ((2 * k) - 1)^(2))" a1="k" a2="1" a3="n"/>
<output a0="f"/>
</command>
<element type="function" label="f">
<show object="false" label="true" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
</element>
<command name="Min">
<input a0="f" a1="0" a2="10"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.712388980389274" y="-1" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="a" exp="y(A)" />
<element type="numeric" label="a">
<value val="-1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="g" exp="g(x) = f(x) - a" />
<element type="function" label="g">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
</element>
<expression label="h" exp="h(x) = g(x)^(2)" />
<element type="function" label="h">
<show object="true" label="true" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
</element>
<expression label="b" exp="sqrt(3) / 1.5"/>
<element type="numeric" label="b">
<value val="1.1547005383792515"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<animation speed="1" type="0" playing="false"/>
</element>
<expression label="c" exp="(3 * sqrt(3))"/>
<element type="numeric" label="c">
<value val="5.196152422706632"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<animation speed="1" type="0" playing="false"/>
</element>
</construction>
</geogebra>