functions for finding values

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));

Answer 1

[Andrei Bobrov]

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);

[harley]

thanks, i get the error

??? NaN computed by model function, fitting cannot continue.
Try using or tightening upper and lower bounds on coefficients.

Error in ==> fit at 445
                errstr = handleerr( errid, errmsg, suppresserr );

Error in ==> Untitled at 8
ff = fit(w_int(:),F_int(:),f,'StartPoint',[1 1]);

[Andrei Bobrov]

corrected variable w_int