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matlab的线性拟合工具箱cftool可以很方便的进行曲线的拟合，但如果想实现m文件调用就可以用下面的方法：

%%

clc

clear

close all

%%

% 构造原始数据

x=0:0.02*pi:2*pi;

s=2*sin(3*x+pi/6)+0.7;

plot(x,s),hold on

sr=s+rand(size(s))*0.5;

plot(x,sr,'r--')

%%

% 利用曲线拟合工具箱函数拟合

ft=fittype('A*sin(w*x+f)+c','coefficients',{'A' 'w'

'f' 'c'},'independent','x')

ftop=fitoptions('Method','NonlinearLeastSquares','StartPoint',[2 3

pi/2 1])

[fr,gof,output]=fit(x',sr',ft,ftop)

covalue = coeffvalues(fr)

%%

% 据拟合的参数绘图

sp=covalue(1)*sin(covalue(2)*x+covalue(3))+covalue(4);

plot(x,sp,'g')

legend('precise','interferred','fitresult')

hold off

ft =

General model:

ft(A,w,f,c,x) = A*sin(w*x+f)+c

ftop =

Normalize: 'off'

Exclude: []

Weights: []

Method: 'NonlinearLeastSquares'

Robust: 'Off'

StartPoint: [2 3 1.570796326794897 1]

Lower: [1x0 double]

Upper: [1x0 double]

Algorithm: 'Trust-Region'

DiffMinChange: 1.000000000000000e-008

DiffMaxChange: 0.100000000000000

Display:

'Notify'

MaxFunEvals: 600

MaxIter: 400

TolFun: 1.000000000000000e-006

TolX: 1.000000000000000e-006

fr =

General model:

fr(x) = A*sin(w*x+f)+c

Coefficients (with 95% confidence bounds):

A

= 2.042 (2.003, 2.08)

w

= 2.999 (2.989, 3.01)

f

= 0.5076 (0.4692, 0.546)

c

= 0.9349 (0.9076, 0.9622)

gof =

sse: 1.827767116564399

rsquare: 0.991349326687698

dfe: 97

adjrsquare:

0.991081780090411

rmse: 0.137269661486366

output =

numobs: 101

numparam: 4

residuals: [101x1 double]

Jacobian: [101x4 double]

exitflag: 1

iterations: 6

funcCount: 31

firstorderopt: 2.542006973738076e-005

algorithm: 'Trust-Region Reflective Newton'

covalue =

2.041908361419719 2.999482129378448 0.507597727761528 0.934900585186387

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