Filtered Thermal Noise—Fluctuation of Energy as a Function of Interval Length

Suppose that a source of thermal noise is connected to the input of a band pass filter. Let the output current flow through a resistance of one ohm and observe the energy dissipated in each of a number of intervals. If the intervals are of the same length T, and are taken at random, the energies have a distribution whose average and standard deviation depend upon T. This dependence is studied. Since the results are derived for thermal noise, the question of when noise may be regarded as thermal noise is also considered.