I am doing some pattern recognition research. I have found that a signal power is an important variable in this field of study. However the continuous part of the spectrum (frequency = 0) isn't, and it must be discarded. As a software developer I have wrote computer methods to calculate the power of the alternate (f != 0) part of a signal. To test if my method is correctly implemented I must know if: 1. the energy of a discrete signal is equal to the sum of the squares of the samples? 2. the power of the continuous component of a signal is equal to the square of it's average intensity? 3. the energy of the alternate component of a signal is equal to the sum of the squares of the (samples - average intensity) ? 4. the total signal energy is equal to the sum of the energy of the continuous and alternate components?