Signal correlation vs Pearson correlation between signals I have some data which are the sets of values uniformly distributed along some measure (simple example - along the time intervals).
I tested both the coefficients and found the difference, some times essential.
F.e. if both the data are noise-like, signal r is about 0.7, and Pearson r - about 0.25.

Which coefficient should be considered better and why?

I compute the signal correlation coefficient as
$$
r=\frac{\sum_ix_iy_i}{\sqrt{\sum_ix_i^2}\sqrt{\sum_iy_i^2}}
$$

and Pearson correlation coefficient as
$$
r=\frac{\sum_i(x_i-m_x)(y_i-m_y)}{\sqrt{\sum_i(x_i-m_x)^2}\sqrt{\sum_i(y_i-m_y)^2}}
$$

There are two fragments of pair of signals:

Fragment 1. Two signals with similar Signal- and Pearson- coefficients

Fragment 1 http://net2ftp.ru/node0/nf05@ngs.ru/Signals1.png

Fragment 2. Two noise-like signals: Signal r = 0.7, Pearson r = 0.2

Fragment 2 http://net2ftp.ru/node0/nf05@ngs.ru/Signals2.png

PS I do not need to performe cross-corelation, convolution etc.
Thank robert bristow-johnson for the right question.
In my case signal coefficient shows a some level of similarity between noise-like signals because of appreciable mean values. That is as you compare two electrical noises with some direct voltage: of course they are as more similar as high equal direct voltage they have.
Since I need to compare specifically shapes, I should use Pearson method only (which "normalizes" data itself in terms of mean values).