Energy correlation between natural extra-low-frequency noises at various frequencies

The correlation function is derived for the energy of natural extra-low-frequency noises at the outputs of two extra-low-frequency receivers, each tuned at the input to a different frequency of storm activity in a closed Earth-ionosphere channel. Such a receiver essentially consists of a narrow-band second-order filter, a square-law detector, an integrator, and a recording device for the vertical electric field component, both the bandwidth and integration time being finite. The input signal is a random sequence of radio pulses, with interference of radio waves from neighboring lightning discharges in global storm activity. The spectral characteristics of the output noise are determined from statistical analysis of readings, which depend on the signal processing by the receiver components. The interfrequency correlation coefficient is first calculated for the ideal case of rare single input pulse signals without background radiation, and then for the real case of frequent interfering input pulse signals with ambient noise. The frequency dispersion is found to make estimates of the energy spectrum of signals from lightning distributed in space more accurate and stable than those of the energy spectrum of signals from lightning concentrated at one point.