energy and cross corelllation

[islamatef]

from image below I want answe this question

q1: For the shown 4 signals find thier energies, cross corellation coefficients, and dimension of thier signal space.
can you guess complete orthonomal function set



https://obrazki.elektroda.pl/79_1269515204.jpg

thanks

 

[htg]

The signal space is apparently the space of linear splines, whose dimension is equal to the (number of maxima +number of minima) on the graphs.
To calculate the energy of a signal you have to compute the integral of the square of each signal.
When you divide each signal by the square root of its energy, you obtain normalized signals.
The cross correlation coefficient of two signals equals to the integral of the product of normalized signals.