Peak Width at Half Height

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Laiba Qadeer
Laiba Qadeer on 10 Mar 2020
Commented: Rufus Adjetey on 13 Nov 2020
I started using MATLAB only a few days ago. And I have trouble finding the width of peak. I have two subplots, both of which represent one peak from the data only. I want to know the width of peak at half distance. I also want the line representing width to be displayed on the plot. Please tell me how this can be done.
I searched the internet for help but could not get the desired result.
Here is my code for both graphs:
subplot(2,1,1)
plot(Hwave,Hintense,'.'),title('Original data'),xlabel('Wavelength'),ylabel('Intensity')
axis tight, grid
subplot(2,1,2)
plot(Hwaveinter,Hreal,'.'),title('Eight Times Interpolated Data'),xlabel('Wavelength'),ylabel('Intensity')
axis tight, grid
Thanks
  3 Comments
Laiba Qadeer
Laiba Qadeer on 10 Mar 2020
I have attached the image
Adam Danz
Adam Danz on 10 Mar 2020
Image Analyst's demo will work well with your data.

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Accepted Answer

Image Analyst
Image Analyst on 10 Mar 2020
Edited: Image Analyst on 10 Mar 2020
See this demo:
% Initialization steps.
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
clear; % Erase all existing variables. Or clearvars if you want.
workspace; % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 24;
% Make Gaussian https://en.wikipedia.org/wiki/Gaussian_function
x = linspace(0, 100, 1024);
amp = 50;
mu = 35;
sigma = 20;
y = amp * exp(-(x - mu).^2 / (2 * sigma^2));
hFig = figure;
plot(x, y, 'b-', 'LineWidth', 2);
grid on;
xlabel('x', 'FontSize', fontSize);
ylabel('y', 'FontSize', fontSize);
hFig.WindowState = 'maximized';
% Find the half height - midway between min and max y values.
halfHeight = (min(y) + max(y)) / 2;
hold on;
yline(halfHeight, 'Color', 'g', 'LineWidth', 2);
% Find left edge
index1 = find(y >= halfHeight, 1, 'first');
x1 = x(index1)
line([x1, x1], [0, y(index1)], 'Color', 'r', 'LineWidth', 2);
text(x1+1, 5, sprintf('x1 = %.2f', x1), 'FontSize', fontSize, 'Color', 'r');
% Find right edge
index2 = find(y >= halfHeight, 1, 'last');
x2 = x(index2)
line([x2, x2], [0, y(index2)], 'Color', 'r', 'LineWidth', 2);
text(x2+1, 5, sprintf('x2 = %.2f', x2), 'FontSize', fontSize, 'Color', 'r');
% Compute the full width, half max.
fwhm = x2 - x1
text(mu, halfHeight+2, sprintf('width = %.2f', fwhm), 'FontSize', fontSize, 'Color', 'r', 'HorizontalAlignment', 'center');
caption = sprintf('Full Width, Half Max = %.2f', x2 - x1);
title(caption, 'FontSize', fontSize);
Adapt code as needed for your variable names.
  12 Comments
Image Analyst
Image Analyst on 12 Nov 2020
You data is discrete - it's quantized. There are no elements that are exactly 0.6 for y. So it picks the closest element above that. If you want to interpolate with interp1() or polyval(), you're certainly welcome to do that.
Rufus Adjetey
Rufus Adjetey on 13 Nov 2020
Thank you very much

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