gaussian binning of data

Question

I just have a simple question of how to do gaussian binning for a data point. Lets say that at X = 100 I detect 5000 electrons but my FWHM is like 4 points. Is it possible in matlab to bin the 5000 electrons with a gaussian centered at X = 100. Like 2500 electrons between X = 99 and X = 101 and 5000 between 95 and 105?

Answer 1

It sounds like you have a single measurement at a single point (X=100, e=5000), and also know the value of the FWHM (FWHM = 4).

If this is indeed the case, you can compute the standard deviation sigma like so:

sigma = FWHM/ 2/sqrt(2*log(2));

and you can make bins like so:

[N, binCtr] = hist(sigma*randn(e,1) + X, Nbins);

where N is the amount of electrons in each bin, binCtr are the bin centers, Nbins is the amount of bins you want to use.

If the number of electrons gets large, you could run out of memory. In such cases, it's better to do the same thing but in smaller batches, like so:

% Example data
FWHM = 4;
e = 100000;
X = 100;
Nbins = 100;

% your std. dev.
sigma = FWHM/ 2/sqrt(2*log(2));

% Find where to start with the bin edges. That is, find the point 
% where the PDF indicates that at most 1 electron is expected to fall 
f = @(x, mu, sigma) exp(-0.5*((x-mu)/sigma).^2)/sigma/sqrt(2*pi);
g = @(y) quadgk(@(x)f(x,X,sigma), -inf, y)*e - 1; 
h = fzero(g, X-FWHM*3);

% Create initial bin edges
binEdges = [-inf  linspace(h, 2*X-h, Nbins-2)  +inf];

% Bin electrons in batches
c = e;
done = false;
step = 5e3;
Nout = zeros(Nbins,1);
while ~done

    % electrons still to be binned
    c = c - step;

    % Last step
    if c <= 0
        step = c+step;
        c = 0;
        done = true;
    end

    % Bin the next batch
    N = histc(sigma*randn(step,1) + X, binEdges);   
    Nout = Nout + N;

end

% Bin edges must now be re-defined
binEdges =[...
    2*binEdges(2)-binEdges(3),... 
    binEdges(2:end-1),...
    2*binEdges(end-1)-binEdges(end-2)];