有关matlab中的泰勒级数用法。

运行了下你的代码，语法上并没有问题，如下

检测代码：

clc

clear all

close all

syms x

f1 = (exp(x)+exp(-x))/2;

r = taylor(f1,x,5,0);

disp(r);

输出效果

x^4/24 + x^2/2 + 1

请检查程序上下文，并设置断点单步执行检查中间变量的值是否与预期吻合

我的是2010b，没有这个函数，不过你定义：

----------------------------------------------------------------------------

function

[a0,an,bn]=fseries(f,l,k)

%f为一个周期内的分段函数（分两段，对分两段以上的函数可类似处理）

%2l为周期

%k为近似展开项数，k≥1

%计算傅里叶系数

syms

x

n

L

a0=1/Lint(f(1),-L,0)+1/Lint(f(2),0,L);

an=1/Lint(f(1)cos(npix/L),-L,0)+1/Lint(f(2)cos(npix/L),0,L);

bn=1/Lint(f(1)sin(npix/L),-L,0)+1/Lint(f(2)sin(npix/L),0,L);

%选择作图步长p

if

k>=4

p=fix(k/4);

else

p=1;

end

%绘制4个近似子图

for

i=1:4

f=a0/2+symsum(ancos(npix/L)+bnsin(npix/L),n,1,ip);

f=subs(f,L,l);

subplot(2,2,i),ezplot(f,[-3l,3l]),title(['n=',int2str(ip)])

end

----------------------------------------------------------------------------

测试用例：

输入：

f=sym('[x,0]');

[a0,an,bn]=fseries(f,pi,32)

输出：

a0

=

-1/2L

an

=

-L(cos(npi)+sin(npi)npi-1)/n^2/pi^2

bn

=

-L(-sin(npi)+cos(npi)npi)/n^2/pi^2

这相当于加窗对 x 做滑动平均，挺常见的需求，可以试试下面的代码：

x = (1:20)';

nx = length(x);

% 相邻多少元素取平均

nwin = 9;

% 把 x 折叠成想要的样子。

ncol = nx - nwin + 1;

colindex = 0:(ncol-1);

rowindex = (1:nwin)';

xin = zeros(nwin, ncol, 'like', x);

xin(:) = x(bsxfun(@plus, colindex, rowindex)) % 没加分号，可以看看 xin 折叠成了什么样。

% 把头尾没算的元素插入回 y 里。

padding = fix(nwin/2) - 1;

y = [

    x(1:1+padding);

    mean(xin)';

    x(end-padding:end)

];

也可以用自带的 filter 来处理滑动平均。这种方法灵活性差点，不过对于你的需求正合适。：

x = (1:20)';

nwin = 9;

yout = filter(ones(1, nwin)/nwin, 1, x);

padding = fix(nwin/2) - 1;

y = [

    x(1:1+padding);

    yout(nwin:end);

    x(end-padding:end)

]

依照精度来判别！！！

比方说要算1/（n^2）的和

先确定精度=0001，再来计算

基本方式如下：

clc;clear;

s=0;

e=1;

n=1;

while e>=0001

ss=s;

s=s+1/(n^2)

n=n+1;

e=s-ss;

end

e

这个程序很简单，那么我就不解释了，希望能够帮助到你

syms x

f=25634e+02x^9+25652e+04x^8+11126e+06x^7+27445e+07x^6+42420e+08x^5+42604e+09x^4+27806e+10x^3+11376e+11x^2+26484e+11x^1+26747e+11;

[an,bn,f]=fseries(f,x,9)

an =

[ (534940000000pi + 75840000000pi^3 + 1704160000pi^5 + (54890000pi^7)/7 + (51304pi^9)/9)/pi, - 27841162880pi^2 - 312101856pi^4 - 410432pi^6 - 287993022720, 8114511920pi^2 + 81257616pi^4 + 102608pi^6 + 101588232120, - (900600920960pi^2)/243 - (982273952pi^4)/27 - (410432pi^6)/9 - 35057038158080/729, ((1769650692405pi)/64 + (16836435865pi^3)/8 + (41032827pi^5)/2 + 25652pi^7)/pi, - (4227534952576pi^2)/3125 - (8216261856pi^4)/625 - (410432pi^6)/25 - 1396634790284544/78125, (228828370640pi^2)/243 + (246645872pi^4)/27 + (102608pi^6)/9 + 9100145814680/729, - (11644479251840pi^2)/16807 - (2302917408pi^4)/343 - (410432pi^6)/49 - 7577990404488960/823543, ((115674711229905pi)/16384 + (271842923365pi^3)/512 + (164535327pi^5)/32 + 6413pi^7)/pi, - (74362229720960pi^2)/177147 - (8886433952pi^4)/2187 - (410432pi^6)/81 - 26720932500558080/4782969]

bn =

[ ((1433935166592pi)/5 + (202410805568pi^3)/5 + (18912298608pi^5)/25 + (54707176pi^7)/25 + (12817pi^9)/25)/pi, -((4524504922239pi)/20 + (257431692587pi^3)/10 + (20628307413pi^5)/50 + (27699647pi^7)/25 + (12817pi^9)/50)/pi, ((200007980924032pi)/1215 + (7256209537984pi^3)/405 + (62852615504pi^5)/225 + (55527464pi^7)/75 + (12817pi^9)/75)/pi, -((1303604357887239pi)/10240 + (17458814037587pi^3)/1280 + (337025962413pi^5)/1600 + (111144647pi^7)/200 + (12817pi^9)/100)/pi, (4291895990965568pi^2)/390625 + (13197877258608pi^4)/78125 + (1389827176pi^6)/3125 + (12817pi^8)/125 + 1008779874054206592/9765625, -((421596615384719pi)/4860 + (7444184615281pi^3)/810 + (63435384719pi^5)/450 + (27802183pi^7)/75 + (12817pi^9)/150)/pi, ((307600766143943808pi)/4117715 + (663474242676032pi^3)/84035 + (1036954330992pi^5)/8575 + (389278168pi^7)/1225 + (1831pi^9)/25)/pi, -((343730544769747239pi)/5242880 + (1133513343417587pi^3)/163840 + (5420416582413pi^5)/51200 + (444924647pi^7)/1600 + (12817pi^9)/200)/pi, ((1396563410616444032pi)/23914845 + (5452466891777984pi^3)/885735 + (5147022055504pi^5)/54675 + (500567464pi^7)/2025 + (12817pi^9)/225)/pi]

f =

cos(6x)((228828370640pi^2)/243 + (246645872pi^4)/27 + (102608pi^6)/9 + 9100145814680/729) - cos(7x)((11644479251840pi^2)/16807 + (2302917408pi^4)/343 + (410432pi^6)/49 + 7577990404488960/823543) - cos(x)(27841162880pi^2 + 312101856pi^4 + 410432pi^6 + 287993022720) - cos(3x)((900600920960pi^2)/243 + (982273952pi^4)/27 + (410432pi^6)/9 + 35057038158080/729) + cos(2x)(8114511920pi^2 + 81257616pi^4 + 102608pi^6 + 101588232120) - cos(5x)((4227534952576pi^2)/3125 + (8216261856pi^4)/625 + (410432pi^6)/25 + 1396634790284544/78125) + sin(5x)((4291895990965568pi^2)/390625 + (13197877258608pi^4)/78125 + (1389827176pi^6)/3125 + (12817pi^8)/125 + 1008779874054206592/9765625) - cos(9x)((74362229720960pi^2)/177147 + (8886433952pi^4)/2187 + (410432pi^6)/81 + 26720932500558080/4782969) + (534940000000pi + 75840000000pi^3 + 1704160000pi^5 + (54890000pi^7)/7 + (51304pi^9)/9)/(2pi) - (sin(4x)((1303604357887239pi)/10240 + (17458814037587pi^3)/1280 + (337025962413pi^5)/1600 + (111144647pi^7)/200 + (12817pi^9)/100))/pi - (sin(6x)((421596615384719pi)/4860 + (7444184615281pi^3)/810 + (63435384719pi^5)/450 + (27802183pi^7)/75 + (12817pi^9)/150))/pi + (sin(9x)((1396563410616444032pi)/23914845 + (5452466891777984pi^3)/885735 + (5147022055504pi^5)/54675 + (500567464pi^7)/2025 + (12817pi^9)/225))/pi - (sin(8x)((343730544769747239pi)/5242880 + (1133513343417587pi^3)/163840 + (5420416582413pi^5)/51200 + (444924647pi^7)/1600 + (12817pi^9)/200))/pi + (cos(8x)((115674711229905pi)/16384 + (271842923365pi^3)/512 + (164535327pi^5)/32 + 6413pi^7))/pi + (cos(4x)((1769650692405pi)/64 + (16836435865pi^3)/8 + (41032827pi^5)/2 + 25652pi^7))/pi + (sin(7x)((307600766143943808pi)/4117715 + (663474242676032pi^3)/84035 + (1036954330992pi^5)/8575 + (389278168pi^7)/1225 + (1831pi^9)/25))/pi + (sin(x)((1433935166592pi)/5 + (202410805568pi^3)/5 + (18912298608pi^5)/25 + (54707176pi^7)/25 + (12817pi^9)/25))/pi + (sin(3x)((200007980924032pi)/1215 + (7256209537984pi^3)/405 + (62852615504pi^5)/225 + (55527464pi^7)/75 + (12817pi^9)/75))/pi - (sin(2x)((4524504922239pi)/20 + (257431692587pi^3)/10 + (20628307413pi^5)/50 + (27699647pi^7)/25 + (12817pi^9)/50))/pi

>> an=vpa(an,6)

an =

[ 14570410^12, -5935710^11, 18968910^11, -88255310^10, 50445110^10, -3252510^10, 22677910^10, -16701810^10, 12807410^10, -10130410^10]

>> bn=vpa(bn,6)

bn =

[ 76212810^11, -52155510^11, 36936910^11, -28297710^11, 22862310^11, -19154210^11, 1647110^11, -14442410^11, 12856110^11]

用Matlab对室外温度波进行傅里叶级数拟合可以这样来处理。

1、首先，建立自定义函数，有关傅里叶级数的函数表达式

function y=func(a,n,x) %a——拟合系数，n——阶数，x——自变量

y=傅里叶级数的函数表达式

end

2、必须有x、y对应的数据（十组以上）

3、用拟合函数nlinfit（）求拟合系数

[a,r]=nlinfit(x,y,@(a)func(a,n,x),a0) %a——拟合系数，r——残差，a0——初值

当r约等于0，可以认为拟合是合理的。

fsin=@(n,x) pi/4sign(x)sin(nx);

fcos=@(n,x) pi/4sign(x)cos(nx);

N=20;

Fsin=zeros(1,N+1);

Fcos=zeros(1,N+1);

for n=0:N

Fsin(n+1)=quad(@(x)fsin(n,x),-pi,pi,1e-8)/pi;

Fcos(n+1)=quad(@(x)fcos(n,x),-pi,pi,1e-8)/pi;

end

subplot(211),stem(0:N,Fsin);title('sin');

subplot(212),stem(0:N,Fcos);title('cos');

原来的信号可以表示为[-pi,pi]内的 pi/4sign(x)

反正就是根据傅立叶展开的公式，求原来函数和sinkx，coskx的乘积的积分

上述程序里Fsin  就是  bk

                 Fcos 就是  ak

最后

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