  The short-time Fourier transform (STFT) is a time-frequency representation
widely used in applications, for example in audio signal processing. Recently
it has been shown that not only the amplitude, but also the phase of this
representation can be successfully exploited for improved analysis and
processing. In this paper we describe a rather peculiar pole phenomenon in the
phase derivative, a recurring pattern that appears in a characteristic way in
the neighborhood around any of the zeros of the STFT, a negative peak followed
by a positive one. We describe this phenomenon numerically and provide a
complete analytical explanation.
