Clarification of a formula for MIF

[JXBWk]

To all

I am dealing with a formula and I am hoping that the more mathematically inclined among you might be able to clarify something for me. 

On the attached mcad 15 file there is a formula for a mode indicator function. I am still trying to source the original reference but in the meantime I thought I ask the question.

Could anyone tell me how the sum on the numerator works? Is the formula saying that one has to sum over the entire vector? 

Thanks in advance

Regards

[Werner_E · Accepted solution]

I would see it that way

Actually the absolute value in the nominator isn't necessary as here a real number is squared.

Using vectorization you could also code it in Mathcad like this

The other formula (Breitbach) yields a different result

[JXBWk]

Thanks for the input. I cannot find any paper/text, etc from the quoted "reference". Never mind
The formula yields 1 number. In reality the complex vector is frequency dependant. That is each row is a value at a given frequency
If I got this right if an entry in the complex vector is (near) to imaginary then the MIF should drop (close to zero, drop to a minimum) (at a given frequency)
So one should be able to plot a MIF value at each frequency
Anyway you have answered my original question

[Werner_E]

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@JXBWk wrote:

Thanks for the input. I cannot find any paper/text, etc from the quoted "reference". Never mind

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Would this help

https://pdfcoffee.com/ecss-e-st-32-11c31july2008-pdf-free.html

See 3.2.33

Maybe this paper can be of help, Formula (6) seems to correspond

http://papers.vibetech.com/Paper35-MMIF.pdf

But I have to state that I'm way outside my comfort zone here and have no knowledge of the underlying subject matter.

[JXBWk]

yes that's where the formula I pasted in the mcad file is coming - the ecss reference. This one yields 1 number 

The 2nd ref I am have and is for the Multivariate MIF - uses the H matrix and is an eigenvalue problem ? (or maybe I am confuses with the Complex MIF (CMIF) !)

of interest: 546802.pdf (hindawi.com)

equation 8