Paul F. Fougere

Spontaneous line splitting in maximum entropy power spectrum analysis

Abstract The Burg maximum entropy power spectral estimate yields extremely sharp spectra with high resolution. If the noise level is low, the power spectrum closely resembles a line spectrum. We have discovered, however, that under certain conditions, spontaneous line splitting occurs; lines which should be single split into two or more components. A series of computer experiments using artificial times series was performed with the following results. If the signal length is any multiple of 0.5 cycle there is no splitting for any initial phase of the sine wave; in fact, the spectrum is extremely sharp and stable. The same result applies to a signal length which is an odd multiple of 0.25 cycle but only with an initial phase of 0° or 90°. The splitting is most severe if the signal length is an odd multiple of quarter cycles and the initial phase is an odd multiple of 45°. In this case splitting persists even for signals as long as 49.25 cycles.

The superiority of maximum entropy power spectrum techniques applied to geomagnetic micropulsations

Abstract Several methods of spectrum analysis have been applied to a micropulsation event associated with a magnetospheric substorm. The micropulsations were detected and recorded at Sudbury, Massachusetts, U.S.A. (53.9°N, 357.1°E, geomagnetic coordinates). The data sample is for the period 0630–0900 UT on September 1, 1970 which includes most of an isolated substorm which was preceded by low levels of magnetic activity ( K p = 1°, 0300–0600 UT). Spectra were obtained using 15-min segments of low pass filtered and digitized data for the two horizontal magnetic field components. A dynamic spectrum was obtained by moving the data window by increments of 1 min through the data set. The results show that methods based on the maximum-entropy principle yield higher resolution than the traditional techniques, such as Blackman-Tukey or the discrete Fourier transform using the fast Fourier transform algorithm. Multiplet structure, predicted by recent micropulsation theories, is sharply resolved by maximum-entropy techniques.

Ionospheric radio tomography using maximum entropy: 2. Results of the Russian‐American Tomography Experiment, including the large magnetic storm of November 3–4, 1993

Near the end of the Russian-American Tomography Experiment, November 3 and 4, 1993, the index of magnetic activity (Kp) climbed rapidly from 0 to 7—in a little under 1 day. The quasi-logarithmic Kp index ranges from a low of 0 for very calm conditions to 9 for the most intense magnetic storms. During the course of this magnetic storm the ionospheric response was studied using data collected and analyzed in 28 passes. The results of this intensive study, using contour charts of electron density as well as the three important parameters of the average Chapman profile, the maximum density, the altitude of maximum, and the scale height, are presented. We had dual-frequency receivers set up at four locations on the eastern edge of North America: Block Island, Rhode Island; Hanscom Air Force Base, Massachusetts; Jay, Vermont; and Roberval, Quebec, Canada. Using the dual-frequency (150 and 400 MHz) beacon on the Navy Navigation Satellite System, with a nominal altitude of 1100 km, a tomography pass would typically last about 20 min from horizon to horizon. From a total of 88 passes, 86 passes possessed sufficiently accurate data and have been analyzed using the maximum entropy method, which determines the average vertical profile in the form of an analytical Chapman profile, as well as a set of electron density contours. The Russian tomography experiment, which utilized the same four locations, as well as the incoherent scatter radar results obtained by the Haystack Observatory group, will be discussed at a later date.