傅里叶级数(fourier series)展开的Matlab实现
傅里叶级数(fourier series)展开的Matlab实现MATLAB和maple语言均未直接提供求解fourier级数的系数的直接函数，好我们自己动手丰衣足食，下面提供了一个代码，大家可以参照下
file:///http://latex.codecogs.com/svg.latex?12\,\sin \left( x \right) +3/2\,\sin \left( 2\,x \right) +4/9\,\sin \left( 3\,x \right) +3/16\,\sin \left( 4\,x \right) +{\frac {12}{125}}\,\sin \left( 5\,x \right) +1/18\,\sin \left( 6\,x \right) +{\frac {12}{343}}\,\sin \left( 7\,x \right) +{\frac {3}{128}}\,\sin \left( 8\,x \right) +{\frac {4}{243}}\,\sin \left( 9\,x \right) +{\frac {3}{250}}\,\sin \left( 10\,x \right) +{\frac {12}{1331}}\,\sin \left( 11\,x \right) +{\frac {1}{144}}\,\sin \left( 12\,x \right)给个例子说明下：将函数y=x*(x-pi)*(x-2*pi)，在(0,2*pi)的范围内傅里叶级数展开
syms x
fx=x*(x-pi)*(x-2*pi);
=fseries(fx,x,12,0,2*pi)%前12项展开
latex(f)%将f转换成latex代码
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得到如下结果
an =
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
bn =
[ -12, 3/2, -4/9, 3/16, -12/125, 1/18, -12/343, 3/128, -4/243, 3/250, -12/1331, 1/144]
f =
12*sin(x)+3/2*sin(2*x)+4/9*sin(3*x)+3/16*sin(4*x)+12/125*sin(5*x)+1/18*sin(6*x)+12/343*sin(7*x)+3/128*sin(8*x)+4/243*sin(9*x)+3/250*sin(10*x)+12/1331*sin(11*x)+1/144*sin(12*x)
ans =
12\,\sin \left( x \right) +3/2\,\sin \left( 2\,x \right) +4/9\,\sin \left( 3\,x \right) +3/16\,\sin \left( 4\,x \right) +{\frac {12}{125}}\,\sin \left( 5\,x \right) +1/18\,\sin \left( 6\,x \right) +{\frac {12}{343}}\,\sin \left( 7\,x \right) +{\frac {3}{128}}\,\sin \left( 8\,x \right) +{\frac {4}{243}}\,\sin \left( 9\,x \right) +{\frac {3}{250}}\,\sin \left( 10\,x \right) +{\frac {12}{1331}}\,\sin \left( 11\,x \right) +{\frac {1}{144}}\,\sin \left( 12\,x \right)
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使用论坛的LaTex代码显示如下
http://latex.codecogs.com/svg.latex?12\,\sin%20\left(%20x%20\right)%20+3/2\,\sin%20\left(%202\,x%20\right)%20+4/9\,\sin%20\left(%203\,x%20\right)%20+3/16\,\sin%20\left(%204\,x%20\right)%20+{\frac%20{12}{125}}\,\sin%20\left(%205\,x%20\right)%20+1/18\,\sin%20\left(%206\,x%20\right)%20+{\frac%20{12}{343}}\,\sin%20\left(%207\,x%20\right)%20+{\frac%20{3}{128}}\,\sin%20\left(%208\,x%20\right)%20+{\frac%20{4}{243}}\,\sin%20\left(%209\,x%20\right)%20+{\frac%20{3}{250}}\,\sin%20\left(%2010\,x%20\right)%20+{\frac%20{12}{1331}}\,\sin%20\left(%2011\,x%20\right)%20+{\frac%20{1}{144}}\,\sin%20\left(%2012\,x%20\right)
干得漂亮 牛奔，回去研究一下···谢啦 不是很懂。 下载了研究一下
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