# Should you include division by coefficient of variation in WV reconstruction for its normed 1D signal?

I make a new ECG time series from WV spectrum of original signal and its L2 energy normalisation. I am thinking if the reconstruction step benefits from covariance at each time point. I take later a norm of the matrix, which creates the new time series.

1. result there is no benefit of adding cov postop into the L2 new signal - verified, strong evidence
2. now, testing if the application of cov on the initial energy spectrum helps

## Nonlinearity

I think the coefficient of variation should not be applied to the initial spectrum because there exists a bijection between the two data sets, although a nonlinear one.

The problem here is that neither sensor is better in this case, because the data sets are direct conversions of each other, but the CV of each data set is different: 0.79 versus 0.42.

Hovever, I am not sure if the nonlineary of the problem case makes the thing different.

• Could i have the delight of an image of the time series you are having fun with?... – Brethlosze Nov 4 '16 at 17:49
• Well.. being privated of that delight.........Yes, granted, that is nonlinear, but no more nonlinear that a windowed squared (ambiguity function :) ). Given that, having different CV or covariances or whatever differences, is not a surprise. – Brethlosze Nov 4 '16 at 17:57
• Well ive not proposed anything yet :). You have the CV for each x1(t) and x2(t).. But what do you want to do now?. What is what you need to test? – Brethlosze Nov 4 '16 at 18:18
• Well... that will depend on the quality of the fitness, my friend... Maybe you just need to reconstruct and then just make the corr test, or maybe do partial tests first as you suggest. Indeed this is an optimization problem including cov+corrs at each stage. Because you are not sure -and we are clear about that- i think you need to define which is the problem required to being solved... and capisco, you got it. No rocket science at all.... If you put on the table more details, i could assist you further. Now i am just supposing in what you are involved. – Brethlosze Nov 4 '16 at 18:46
• And some frustrated PhD told me that i should integrate two times for obtaining geolocations. I guess it depends on how you apply that COV dont you think? – Brethlosze Nov 4 '16 at 19:00

There is no benefit of dividing the new improved signal by the covariance of the original ECG and its improved signal like the following code; by the two decimal accuracy in Corrgrams and other more precise tools (eigen cor)

% Covariance http://dsp.stackexchange.com/q/35291/5633
% https://en.wikipedia.org/wiki/Coefficient_of_variation
utp = utp / sum( cov(u,utp) )';

Fig. 1 Left-hand-side figure without division by covariance and Right-hand-side figure with division by covariance - about marginal dependence and independence of the cases

Other inspected methods where I see no difference

• Eigen cor matirx of the two
• -M^{-1} about conditional independence and dependence

Please, let me know how to get more decimal digits in R corrgram panel.cor; I am trying to replace the problem by Didzis' p-value corrgram discussed there but having problems with finding the upper bound for the amount of points to maintain significant p-value.

• Hi my friend... That is obvious, dividing by the CV will got anything new. I am still waiting for something more.... substantial.. How could i improve your optimization results if we.... dont have an idea of how they are? – Brethlosze Nov 5 '16 at 18:08
• @hypfco Next thing which I will do is to measure segmental correlation levels, and learn the beahivor. I can reach significant results even with 7M points. I am thinking how to study the number of points vs significance. - - I will just use the measurement data from the beginning to the end and then take things segmentally. By stratified data, I can then explain if there is some strange behivior. - - The reconstruction is basically a redefined form of Moyal generalized form. – Léo Léopold Hertz 준영 Nov 5 '16 at 19:40
• Well, good luck with that!.... If you have a clear question on here, you should raise it. By the way, this question could surely go on hold, for stopping traking it... – Brethlosze Nov 12 '16 at 7:29