Hi, I am having a bit of a problem regarding a simple proof for a generic energy signal, the question reads as thus: For an energy signal g(t) with energy Eg, show that the energy of any one of the signals -g(t), g(-t) and g(t-T) is Eg. Show that the energy of g(at) is Eg/a. While I can arrive at the answers intuitively, the total area under the curve is constant for the first parts and is being reduced or increased for the second part, I cant figure out how to mathematically prove any of these except the case of -g(t). I am starting with the basic definition of the energy signal Eg=integral(g(t)^2,t,-inf,inf) but I cant figure out a way to get any further without an actual function.Can anyone give me any guidance? Thanks so much.
For all the other ones, you should use an appropriate change of variables. Look at the definition of Eg for the specific g given and think about what a good choice for a change of variable would be.