functions for finding values
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how and what MATLAB functions could i use to find/verify the value of 'a', like i have done using the cubic spline method. (i am pretending that i don't know what that value is)
a=5;
w=-a:a/1000:a;
F=2*sin(a*w)./w;
%
%
w_int=-5:0.01:5;
F_int=spline(w,F,w_int);
plot(w_int,F_int,'o');
plot(w,F, '--', w_int,F_int,'o')
c = max(F_int);
[~, idx] = min(abs(w_int - 0.005));
d = w_int(idx);
a1 = (c*d)/(2*sin(d));
采纳的回答
Andrei Bobrov
2013-8-22
编辑：Andrei Bobrov
2013-8-23
Use Curve Fitting Toolbox
a=5;
w=-a:a/1000:a;
F=2*sin(a*w)./w;
%
w_int=-5:0.01:5;
w_int(abs(w_int) < eps(1e3)) = [];
F_int=spline(w,F,w_int);
solution:
f = fittype('a2*sin(a1*x)./x');
ff = fit(w_int(:),F_int(:),f,'StartPoint',[1 1]);
out = ff.a1
OR use Statistics Toolbox
a=5;
w=-a:a/1000:a;
F=2*sin(a*w)./w;
%
w_int=-5:0.01:5;
F_int=spline(w,F,w_int);
mf = @(b,x)b(2)*sin(b(1)*x)./x;
b_out = nlinfit(w_int,F_int,mf,[1; 1]);
out = b_out(1);
AND variant with Optimization Toolbox
xdata=(-5:0.01:5)';
ydata=spline(w,F,xdata);
t = abs(xdata) < eps(1e4);
xdata(t) = [];
ydata(t) = [];
f = @(a,xdata)a(2)*sin(a(1)*xdata)./xdata;
x = lsqcurvefit(f,[1; 1],xdata,ydata);
out = x(1);
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