Effects of Frequency Averaging on Estimates of Plasma Wave Coherence Spectra

The effects of frequency averaging (i. e., data smoothing) on digitally computed plasma-wave coherence-spectra are investigated. Such averaging, or smoothing, of the data is necessary to reduce the variance of the spectral estimators to acceptable levels. However, too much averaging results in a loss of frequency resolution and in an "artificial" reduction of the degree of coherence characterizing each wave in the fluctuation spectrum. This latter problem is the subject of this paper and is concluded that in order to avoid such difficulties, it is necessary: (1) that the averaging bandwidth be small compared to the spectral bandwidth of the wave packet, and (2) that the distance between the two spatial monitoring points be small compared to the coherence length of the wave packet.