How can I fit a second Fourier component to a polar histogram?

I would like to fit a second Fourier series function: E(x) = (1/2*pi)*(1+A1*cos(2*xdata-A2))

to

theta = atan2(rand(100000,1)-0.5,2*(rand(100000,1)-0.5)); polarhistogram(theta,25);

Regards, Eric

Answer 1

[David Goodmanson]

Hi Eric, see how this works. I added an adjustable tilt angle to the random data to test the fit. The code compares the fit to the unnormalized histogram, with its total of 1e5 points. To go to the normalized expression you have, then A1 = B1/c(n0) and A2 = -B2.

npts = 1e5;
n = 25;   % should be odd
tilt = pi/4;
theta = atan2(rand(npts,1)-0.5,2*(rand(npts,1)-0.5)) + tilt;
theta = mod(theta+pi,2*pi)-pi;
h = polarhistogram(theta,n);

% start fit
val = h.Values;
c = fftshift(fft(ifftshift(val)))/n;   % fourier coefficients
% n0 is index for constant term.  c(n0) = npts/n = average bin value
n0 = (n+1)/2;    
B1 = 2*abs(c(n0+2));
B2 = angle(c(n0+2));
theta1 = (h.BinEdges(1:end-1) + h.BinEdges(2:end))/2;   % bin centers
E = c(n0) + B1.*cos(2*theta1 + B2);
hold on
polarplot(theta1,E,'-o')
hold off

[Eric Gbadam]

Hi David, Thank you for the reply. For some reason, the Matlab is returning an error code that looks strange. It says it can't find the polarhistogram function:

>> h=polarhistogram(theta,n); Undefined function or variable 'polarhistogram'

Let me restart my machine and see what happens next.

[Eric Gbadam]

David, I get this error message anytime I run the code

Undefined function or variable 'polarhistogram'.

Error in polarfit (line 6) h = polarhistogram(theta,n);

[David Goodmanson]

Hi Eric, what version of matlab are you using? This seems a bit odd since your original question contains that function.