Signal energy estimation

[greka]

It would be great if we found a new (unknown to me) way of signal energy estimation.

There are two ways I'm aware of:

[greka]

Both ways gives approximately good results on a sample speech signal:

[greka]

And by varying minimum energy threshold it's possible to make decision about is signal interval "energy-intensive" or not:
(red means "low energy" and blue - energy-intensive)

[greka]

as we may notice (first energy estimate picture) there are voiced parts which are hidden from our math-model :(

And the meaning is following:

high-frequency signal with low amplitude (like hissing, whistling) described as energy-intensive while

high amplitude signal (sometimes) considered as low-energy.

:(

And my question is:
is there any mechanism which handles such situation more accurate than 2 formulas stated above?

[greka]

picture#1: "high frequency" described as "high-energy" signal

picture#2: "low frequency, high amplitude" described as "low-energy" signal

[MAX]

picture#1: "high frequency" described as "high-energy" signal

picture#2: "low frequency, high amplitude" described as "low-energy" signal

Garegin, Fourier nujno delat'.

[greka]

Fourier в чистом виде слишком много времени на расчеты требует.

синусы, коксинусы..

есть спец. версии - дискретное Фурье-преобразование, косинус Фурье-преобразование - но энто не то.

А за PDF с подробным описание расчетов энергий сигналов - отдельное спасибо, я тебе уже говорил, повторюсь: спасибо.
:)

[PoKo]

You should calculate the spectral density of the Noise signal, then you have to integrate in the frequency range you are interested in, you will get the power of the signal. By much proper analysis you can locate the sources of that noise. The Fourier transform is not so difficult to carry out if you have the data in matrix form, you can save it in ASCII format and then import data into one of the available mathematical packages for further processing. All depends on what exactly do you want to do and why you need to calculate the energy of the signal. If it is related with data encrypting into noise signal it is much more complicated task.

[greka]

PoKo, thanks for the reply.
So, you offered to calculate the spectral density - Fourier calculation, isn't it?

[PoKo]

If you do not have good spectrum analyzer with soft. You should make Fourier transform of the given data, then multiply the function by its conjugate [actually you should average by statistical ensemble too, but you can skip that] and draw the graph. The integral of the curve will yield the power of the signal in the frequency range you measured your signal. But generally, good data encryption into noise signal is processed under frequencies unreachable for analysis in the countries of the third world or developing countries (russia included).

[libertyfreedom]

may someone tell me how I can find a good mathematical ebook in signal processing