# Energy of compressed signals

I have tried a code to compress a signal using Compressed Sensing(CS). The input signal is $$x$$ and the compressed signal $$y$$ is given by : $$y=Φ*x$$ where $$Φ$$ is the sensing matrix.
I have used the following matlab function to compute the energy of $$x$$ and the energy of $$y$$ .

energy_x= sum(x(1:384,:).^2);
energy_y = sum(y(1:192,:).^2);

The length of $$x$$ is 384 , and the length of $$y$$ is 192.
I found that the energy of $$x$$ is 446910 and the energy of $$y$$ is 77651282 .
Is it is reasonable to obtain higher energy for the output than the input?

• i think that these is related to scale. is there a difference between ones(1,100) and 50*ones(1,100)? information wise – user28715 Oct 25 '18 at 15:23

Without information on $$Φ$$, you can obtain almost anything, since $$\lambda Φ$$ could be a valid CS matrix as well. Generally, one imposes structure contraints, such as unit energy for their rows or columns.