How to calculate the width where the intensity is higher than 20% of the maximum intensity?

To do this, I think I have to utilize the findpeaks function. Then interpolate the 20% to the full width at half maximum (FWHM). So we can find its width?

Below is the code for an attempt to get the max intensity and its FWHM:

[pks,widths] = findpeaks(Int,x2,'NPeaks',1,'WidthReference','halfheight');

Answer 1

[Mathieu NOE]

hello Angelo

I have no doubt you can use findpeaks

but sometimes I prefer my own way.

see demo below - this is to find W20 and extract the portion of data between the two crossing points

NB that the function crossing_V7 use linear interpolation which is more accurate (on the x axis) then simply finding the first x data element above 20% (this depends of your x spacing)

hope it helps

clc
clearvars

%  data
load('position.mat');
x = x2; clear x2
load('Intensity.mat');
y = Int; clear Int

threshold = 0.2*max(y); % 20% of peak amplitude

[t0_pos1,s0_pos1,t0_neg1,s0_neg1]= crossing_V7(y,x,threshold,'linear'); % positive (pos) and negative (neg) slope crossing points 
% ind => time index (samples)
% t0 => corresponding time (x) values 
% s0 => corresponding function (y) values , obviously they must be equal to "threshold"

% depending of the threshold level we have either one or three peaks 
% if we have 3 peaks then pick the second one
if numel(s0_pos1) >1
    s0_pos1 = s0_pos1(2);
    s0_neg1 = s0_neg1(2);
    t0_pos1 = t0_pos1(2);
    t0_neg1 = t0_neg1(2);
end
    


% x difference between t0_neg and t0_pos = W20
W20 =  t0_neg1 - t0_pos1

% extract the data and do interpolation 
xx = linspace(t0_pos1,t0_neg1,100);
yy = interp1(x,y,xx);

figure(1)
plot(x,y,'b',t0_pos1,s0_pos1,'dr',t0_neg1,s0_neg1,'dg',xx,yy,'linewidth',2,'markersize',12);grid on
legend('signal','signal positive slope crossing points','signal negative slope crossing points','selected data');
xlim([-6e-4 6e-4]);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [t0_pos,s0_pos,t0_neg,s0_neg] = crossing_V7(S,t,level,imeth)

% [ind,t0,s0,t0close,s0close] = crossing_V6(S,t,level,imeth,slope_sign) % older format

% CROSSING find the crossings of a given level of a signal
%   ind = CROSSING(S) returns an index vector ind, the signal
%   S crosses zero at ind or at between ind and ind+1
%   [ind,t0] = CROSSING(S,t) additionally returns a time
%   vector t0 of the zero crossings of the signal S. The crossing
%   times are linearly interpolated between the given times t
%   [ind,t0] = CROSSING(S,t,level) returns the crossings of the
%   given level instead of the zero crossings
%   ind = CROSSING(S,[],level) as above but without time interpolation
%   [ind,t0] = CROSSING(S,t,level,par) allows additional parameters
%   par = {'none'|'linear'}.
%	With interpolation turned off (par = 'none') this function always
%	returns the value left of the zero (the data point thats nearest
%   to the zero AND smaller than the zero crossing).
%


% check the number of input arguments
error(nargchk(1,4,nargin));

% check the time vector input for consistency
if nargin < 2 | isempty(t)
	% if no time vector is given, use the index vector as time
    t = 1:length(S);
elseif length(t) ~= length(S)
	% if S and t are not of the same length, throw an error
    error('t and S must be of identical length!');    
end

% check the level input
if nargin < 3
	% set standard value 0, if level is not given
    level = 0;
end

% check interpolation method input
if nargin < 4
    imeth = 'linear';
end


% make row vectors
t = t(:)';
S = S(:)';

% always search for zeros. So if we want the crossing of 
% any other threshold value "level", we subtract it from
% the values and search for zeros.
S   = S - level;

% first look for exact zeros
ind0 = find( S == 0 ); 

% then look for zero crossings between data points
S1 = S(1:end-1) .* S(2:end);
ind1 = find( S1 < 0 );

% bring exact zeros and "in-between" zeros together 
ind = sort([ind0 ind1]);

% and pick the associated time values
t0 = t(ind); 
s0 = S(ind);

if ~isempty(ind)

    if strcmp(imeth,'linear')
        % linear interpolation of crossing
        for ii=1:length(t0)
            %if abs(S(ind(ii))) >= eps(S(ind(ii)))    % MATLAB V7 et +
            if abs(S(ind(ii))) >= eps*abs(S(ind(ii)))    % MATLAB V6 et -    EPS * ABS(X)

                % interpolate only when data point is not already zero
                NUM = (t(ind(ii)+1) - t(ind(ii)));
                DEN = (S(ind(ii)+1) - S(ind(ii)));
                slope =  NUM / DEN;
                slope_sign(ii) = sign(slope);
                t0(ii) = t0(ii) - S(ind(ii)) * slope;
                s0(ii) = level;
            end
        end
    end

    % extract the positive slope crossing points 
    ind_pos = find(sign(slope_sign)>0);
    t0_pos = t0(ind_pos);
    s0_pos = s0(ind_pos);

    % extract the negative slope crossing points 
    ind_neg = find(sign(slope_sign)<0);
    t0_neg = t0(ind_neg);
    s0_neg = s0(ind_neg);

else

    % empty output
    ind_pos = [];
    t0_pos = [];
    s0_pos = [];

    % extract the negative slope crossing points 
    ind_neg = [];
    t0_neg = [];
    s0_neg = [];
    
end

end

[Lope]

@Mathieu NOE Thank you so much! This really helps. Thank you also for the extra effort in giving explanations for the entire process.

[Mathieu NOE]

My pleasure !