Can someone explain how they got from equation 11 to equation 14?

[tom2357]

 

[topsquark]

Reading this is like trying to read Sumerian. I don't even know what subject this is! Can you please define your terms?

-Dan

 

[blamocur]

It's been awhile since I looked at Shannon's theory, so I don't know how they get from (11) to (12) -- probably exploiting some properties of [imath]H[/imath].
To get from (12) to (13) you observe that [imath]\dot{E_1} = -\frac{1}{\zeta} E_1 = -\frac{E_1}{{SNR}}[/imath]
Getting from (13) to (14) seems pretty straightforward, but let us know if you have difficulty there too.

 

[tom2357]

I substituted the equation for E₁ and then applied the product rule of differentiation followed by Leibnitz's rule for integration on the second term and ended up with equation 14. I don't know the details of the paper either as a friend of mine requested me to solve this, but I felt like it's a straightforward differentiation question and since I couldn't find it in the morning I posted it here.

 

[tom2357]

Reading this is like trying to read Sumerian. I don't even know what subject this is! Can you please define your terms?

-Dan

The variable in question is SNR and we just need to reach from 11 to 14. The explanation of the terms or the background is not necessary for me. I just need to prove it. Think of this as a pure mathematics problem instead of an engineering one.

 

[topsquark]

The variable in question is SNR and we just need to reach from 11 to 14. The explanation of the terms or the background is not necessary for me. I just need to prove it. Think of this as a pure mathematics problem instead of an engineering one.

We need more information! Now that blamocur made a mention of Shannon's theory I could at least Google some of it. But we still don't know what [imath]\mathbb{E}[/imath] or H are. Without that there is no way to get from 11 to 12.

Please tell us what the terms in the equation are.

-Dan

 

[Deleted member 4993]

We need more information! Now that blamocur made a mention of Shannon's theory I could at least Google some of it. But we still don't know what [imath]\mathbb{E}[/imath] or H are. Without that there is no way to get from 11 to 12.

Please tell us what the terms in the equation are.

-Dan

But we still don't know what E or H are

Could those be electromotive and/or magnetic field properties?

It says "The capacity in bits/s/Hz is then [18], [19]...." Are those pointing to references at the end of the paper? If it is then it will be nice if you included those!!!

 

[blamocur]

Could those be electromotive and/or magnetic field properties?

It says "The capacity in bits/s/Hz is then [18], [19]...." Are those pointing to references at the end of the paper? If it is then it will be nice if you included those!!!

It looks like stuff from digital communications, where the capacity refers to a channel capacity, and (11) looks very much like https://en.wikipedia.org/wiki/Shannon–Hartley_theorem. But the derivation of (12) from (11) is beyond me. @tom2357 says "The explanation of the terms or the background is not necessary for me.", but I cannot say the same about myself, which means I cannot help him beyond what I've already posted.