  Several analysis methods for nonstationary fluctuations are described and
applied to the edge localized mode (ELM) instabilities of limiter H-mode
plasmas. The microwave scattering diagnostic observes poloidal $k_{\theta}$
values of 3.3 cm$^{-1}$, averaged over a 20 cm region at the plasma edge.A
short autoregressive filter enhances the nonstationary component of the plasma
fluctuations by removing much of the background level of stationary
fluctuations. Between ELMs, the spectrum predominantly consists of broad-banded
300-700 kHz fluctuations propagating in the electron diamagnetic drift
direction, indicating the presence of a negative electric field near the plasma
edge. The time-frequency spectrogram is computed with the multiple taper
technique. By using the singular value decomposition of the spectrogram, it is
shown that the spectrum during the ELM is broader and more symmetric than that
of the stationary spectrum. The ELM period and the evolution of the spectrum
between ELMs varies from discharge to discharge. For the discharge under
consideration which has distinct ELMs with a 1 msec period, the spectrum has a
maximum in the electron drift direction which relaxes to a near constant value
%its characteristic shape in the first half millisecond after the end of the
ELM and then grows slowly. In contrast, the level of the fluctuations in the
ion drift direction increases exponentially by a factor of eight in the five
milliseconds~after the ELM. High frequency precursors are found which occur one
millisecond before the ELMs and propagate in the ion drift direction. These
precursors are very short ($\sim 10 \mu$secs), coherent bursts, and they
predict the occurrence of an ELM with a high success rate.
