Full Wave Half Maximum function

[exile303]

Dear all,

I am currently trying to find the formula to help me compute the FWHM for the given xy data.

But,

I only managed to get the first half maximum using

=Index(1:2,1,Match(C6,2:2,1)),

I have been troubleshooting for few hours and has yet to find any solution to find the 2nd half.

May I ask for help in regards to this,
Many thanks.

[AliGW]

Welcome to the forum!

What is the FWHM for the given xy data? What exactly are you trying to do?

[anupsubudhi]

hi,
if you can provide a sample worksheet for this problem, that will help a lot to understand and answer your question.

regards
anup

[José Augusto]

Hi

Suppose your xy data in B1:AO2

To get the value of x that correspond to the first (second ...) max of B2:AO2 try this array formula

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and copy down.

Note: ...confirmed by pressing CTRL+SHIFT+ENTER to activate the array, not just ENTER. You will know the array is active when you see curly braces { } appear around your formula. If you do not CTRL+SHIFT+ENTER you will get an error or a clearly incorrect answer.

See the file

[exile303]

Hi,
Thank you for your responses,

Let me start by explaining what I am trying to do,

fwhm.PNG

As drawn in the picture,

I have a data of xy data where I am trying to take in the value of the half minimimum in this case,

And take in the width of the purple color as in x value,

I was only managed to get the value of the first half minimum (x value) using this,
=Index(1:2,1,Match(C6,2:2,1)),

And I am hoping to look for help for the 2nd half minimum to get the (x value),

PS I am trying to review on solution posted by Mr Jose but still kind of confused.

Thank you,
Best regards.

[exile303]

And Sorry,
C6 should be =A6/2 for this case.

[MrShorty]

I think your Full Wave Half Maximum description through me off. What I see you describing is full width half maximum (https://en.wikipedia.org/wiki/Full_w...t_half_maximum ). What specifically do you need help with? Here's what I would probably do:

1) Finding the Maximum (well, minimum in your case), should be easy since your signal data is fairly clean. If you believe it is clean enough, something like =MIN(2:2) will find the minimum of row 2 data. Similar for row 4. If you think you will need something more complex (from noisy data, for example), then we can figure out what that should be.
2) Excel, unfortunately, does not have a nice build in linear interpolation function, but I think I would solve for the two x values at half height using a linear interpolation algorithm. I know I have seen a linear interpolation VBA UDF somewhere on this forum (https://www.excelforum.com/excel-pro...ml#post2772517 ). Again, you example shows some pretty clean data. If the data are too noisy, something more elaborate may be needed. At this point, only you know how noisy your data will be.
2a) Use a lookup function to locate the minimum found in step 1.
2b) Select two x "guesses" on either side of the minimum.
2c) Use a numerical algorithm (something like Solver in Excel) and a linear interpolation function to find where y=min/2 by changing x. You will have to run it twice -- once for each side of the minimum.
3) At that point, the width is simply the difference of the two x values.

That's an overview of how I would do something like this. Is there a specific step you have trouble with?

[exile303]

Thank you MrShorty for your response,

I am only trying to take in approximate value of FWHM for 2 x values,

I am not pretty sure about what Linear interpolation is for now, I will try to look into it.

=INDEX(1:2,1,IFERROR(MATCH(MIN(2:2)/2,2:2,-1),MATCH(MIN(2:2)/2,2:2,-1)))

I was able to find the first half of x which is 2001.685 using the above function,

But unable to write another function which help me find the 2nd x value on the other side which approximately would be about 2001.743,

I am not looking for any complicated code that help me compute the exact value.

Sorry, I am quite a new learner in excel function and vba coding.
I hope you can advise me on this,

Thank you,
Best regards.

[José Augusto]

Hi

To find the correspondent value of A6/2 you can use the following array formula

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Please, confirmed by pressing CTRL+SHIFT+ENTER to activate the array, not just ENTER. You will know the array is active when you see curly braces { } appear around your formula. If you do not CTRL+SHIFT+ENTER you will get an error or a clearly incorrect answer.

[exile303]

Hi

To find the correspondent value of A6/2 you can use the following array formula

Please Login or Register  to view this content.

Please, confirmed by pressing CTRL+SHIFT+ENTER to activate the array, not just ENTER. You will know the array is active when you see curly braces { } appear around your formula. If you do not CTRL+SHIFT+ENTER you will get an error or a clearly incorrect answer.

Hi Mr Jose Augusto,

Yes,
The result is similar to my function,

May I ask if your function could be altered to find the 2nd correspondent value on the right side of the graph??

Thank you,
Best regards.

[MrShorty]

I think either your function or Jose Augusto's function would work for the other side if you had a copy of the data that was sorted in the opposite direction. If you need Excel to sort for you, Excel will want the data going down rows instead of across columns, so you will need to transpose the data. Transpose is one of the options in paste special, so it should not be overly difficult. Try using that function on two copies of the data. One copy sorted in "ascending" order by x, another copy sorted in descending order by x. The formula applied to the first copy of the list will give you the "left" value. The formula applied to the second copy will give the "right" value.

Will that work for you?

[José Augusto]

Hi

The formulas are in the file I attach.

My propose for the solution is:

1) Find Minimum y: -15,084 in column 6715 that correspond to x=2001,714

2) Find Minimun y/2: -7,542 in column 6743 that correspond to x=2001,742

3) Find the next value of y in next position that is -7,288 in column 6744 that correspond to x=2001,743 (so we are in the right side, ascending curve)

4) Find simetric to Min in the left side of curve -7,563, x=2001,686 in position 6687

5) Iterate in this neighborhood (iteration value in G6) to find the closest value of the other Min / 2 (the same as in 4))

See the file
Same formulas are array formulas

[José Augusto]

Hi

I found another way, more simple, to solve the problem.

$B7=MIN(2:2)

Determine a₁ such that y = B7 / 2 ± a₁ is the minimum of the table, closer to B7 / 2 in the left part of the graph
Array formula for the left side of the graph:

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Do the same in the right part of the graph
Array formula for the right side of the graph:

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Determine the 4 values y = B7 / 2 ± a_i
Determine the x correspondent values of that four values.

See the file

[exile303]

Dear Mr Jose Augusto,

Thank you very much for your help,

I will try to analyze the formula that is given to me,

I really appreciate your help =),
Best regards.

[José Augusto]

You're welcome

I'm happy to have helped.