How to plot a lorentzian peak with known hwhm, position and height?

Hi,

I would like to plot a graph to how the deconvolution of an FTIR spectrum. I've fitted the peaks with a separate program and I have the peak information for the individual peaks (hwhm, position and height).

There doesn't seem to be a simple lorentzian function on matlab as far as I can see?

Note: I am not trying to fit any data, I'm trying to plot stand alone lorentzian peaks to break down a spectrum.

I'm made the following function:

function y = lorentz(x, pos, h, H)
num =  H*0.5;
den = ( x - pos ).^2 + (0.5 * H).^2;
y = h* num*(den.^-1)*(pi).^1;

end    

and used the following code to plot it:

x = linspace (3100, 3700, 1000);
pos = 3624;
h = 0.7945223;
H = 2.003005*2;

d = lorentz(x, pos, h, H);

plot(x, d)

But the height of the function is not the correct height.

Answer 1

[Tiarnan Murphy]

The maximum height of a Lorentzian distribution is:

Where HWHM is the half width at half the maximum height.

In the case of your code this is:

If you wanted to scale this to a specific height then you could use the following function, which I believe should work.

function y = lorentz(x, position, half_width_half_max, height)
    % A function to plot a Lorentzian (a.k.a. Cauchy) distribution given a
    % space vector 'x', a position and a half width at half maximum.
    % The distribution is then scaled to the specified height.

    if nargin <=2
        errordlg(["At least three input arguments are required.";...
            "These must be in the order x_space, position, half_width.";...
            "An extra height argument can be added to change scale."],...
            "Input Error")
    end

    y = 1 ./ (half_width_half_max.*...
        (1+((x-position)./half_width_half_max).^2));
    
    if nargin == 3
        height = max(y);
    end
    
    y = y.*(height/max(y));
    
end