How find FWHM for large numbers of plots?

Here simply if i want to write the matlab code to find the fwhm (up to 4 or 5 digits) of like following curve, i have to find x values difference corresponding to average value of y. Since x values at average y do not lie at y data points hence i required interpolate values of x. Pls help regarding to this.

for example take below plot and data

clear all 
clc
y=[];
for x=-4:5;
z=x.^2;
y=[y z];
end
y;
x=-4:5;
plot(x,y)

Here i have to find x values difference at y=12.5 to determine the fwhm ,of respective curve. How can i write in code?

Thank you.

Answer 1

[Star Strider]

Try this:

x=-4:5;
for k = 1:numel(x)
    z=x(k).^2;
    y(k) = z;
end

[miny,idx] = min(y);
left_x = interp1(y(1:idx),x(1:idx), y(1)/2)
right_x = interp1(y(idx:end),x(idx:end), y(1)/2)

figure
plot(x,y)
hold on
plot([left_x right_x], [1 1]*y(1)/2, '+r')
hold off

There is no ‘full width-half-maximum’ because ther is no defined maximum. This code finds the approximate values for ‘full-width-half-minimum’ instead, since only that makes sense in this context.

.

[MOHD UWAIS]

Thank you

For me it will be more beneficial in terms of maximum value of y. If i cosider maximum value of y 25, what will be change?

[Star Strider]

My pleasure!

The changes would be:

left_x = interp1(y(1:idx),x(1:idx), y(end)/2)
right_x = interp1(y(idx:end),x(idx:end), y(end)/2)

and in the plot call:

plot([left_x right_x], [1 1]*y(end)/2, '+r')

since here, the maximum value of ‘y’ is equal to ‘y(end)’. Make the appropriate changes to get the result you want, using whatever values of ‘y’ you want.

Alternatively:

left_x = interp1(y(1:idx),x(1:idx), max(y)/2)
right_x = interp1(y(idx:end),x(idx:end), max(y)/2)

and:

plot([left_x right_x], [1 1]*max(y)/2, '+r')

to use the maximum in a particular data set.

.

[MOHD UWAIS]

thanks a lot

[MOHD UWAIS]

can i choose max y (not y(1)) on left side in a particular data set?

[Star Strider]

As always, my pleasure!

It would likely be best to use ‘max(y)’.