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个函数</span><span
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amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>展开=
为傅立叶级数:</span></p>
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pt'><span
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font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>其实就是要求出ࠥ=
4;中的系数</span><span
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"Times New Roman";mso-hansi-font-family:"Times New Roman"'>和</span><=
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amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>,根=
据三角函数系的正交=
4615;,我们可以得到它ߤ=
4;的计算公式如下:</span></=
p>
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<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>这样,结合</span><span
class=3DSpellE><span lang=3DEN-US>Matlab</span></span><span style=3D'font-f=
amily:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>的积分命令</span><span
class=3DSpellE><span lang=3DEN-US>int</span></span><span lang=3DEN-US>()</s=
pan><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>就可以计算这些=
系数,从而就可以进=
4892;函数的傅立叶展开ߚ=
2;。</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>例</span><span lang=3DEN-US>6</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>:求函数</span><span lang=3DEN-U=
S><sub><!--[if gte vml 1]><v:shape
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amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>在</span><=
span
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</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>上的=
傅立叶级数。</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>解:先求出傅立ࡥ=
4;系数,程序如下:</span></=
p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
class=3DGramE><span lang=3DEN-US>clear</span></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
class=3DSpellE><span class=3DGramE><span lang=3DEN-US>syms</span></span></s=
pan><span
lang=3DEN-US> x n</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>f=3Dx^2</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>a0=3D<span class=3DSpellE><span class=3DGramE>int</span></span=
><span
class=3DGramE>(</span><span class=3DSpellE>f,x,-pi,pi</span>)/pi</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
class=3DGramE><span lang=3DEN-US>an=3D</span></span><span class=3DSpellE><s=
pan
lang=3DEN-US>int</span></span><span lang=3DEN-US>(f*<span class=3DSpellE>co=
s</span>(n*x),x,-<span
class=3DSpellE>pi,pi</span>)/pi</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
class=3DSpellE><span class=3DGramE><span lang=3DEN-US>bn</span></span></spa=
n><span
class=3DGramE><span lang=3DEN-US>=3D</span></span><span class=3DSpellE><span
lang=3DEN-US>int</span></span><span lang=3DEN-US>(f*sin(n*x),x,-<span class=
=3DSpellE>pi,pi</span>)/pi</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>运行结果为:</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
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