We present timing analysis for a Rossi X-ray Timing Explorer observation of
Cygnus X-1 in its hard/low state. This was the first RXTE observation of Cyg
X-1 taken after it transited back to this state from its soft/high state.
RXTE's large effective area, superior timing capabilities, and ability to
obtain long, uninterrupted observations have allowed us to obtain measurements
of the power spectral density (PSD), coherence function, and Fourier time lags
to a decade lower in frequency and half a decade higher in frequency than
typically was achieved with previous instruments. Notable aspects of our
observations include a weak 0.005 Hz feature in the PSD coincident with a
coherence recovery; a `hardening' of the high-frequency PSD with increasing
energy; a broad frequency range measurement of the coherence function,
revealing rollovers from unity coherence at both low and high frequency; and an
accurate determination of the Fourier time lags over two and a half decades in
frequency. As has been noted in previous similar observations, the time delay
is approximately proportional to f^(-0.7), and at a fixed Fourier frequency the
time delay of the hard X-rays compared to the softest energy channel tends to
increase logarithmically with energy. Curiously, the 0.01-0.2 Hz coherence
between the highest and lowest energy bands is actually slightly greater than
the coherence between the second highest and lowest energy bands. We carefully
describe all of the analysis techniques used in this paper, and we make
comparisons of the data to general theoretical expectations. In a companion
paper, we make specific comparisons to a Compton corona model that we have
successfully used to describe the energy spectral data from this observation.Comment: To Be Published in the Astrophysical Journal. 18 pages. Uses
emulatepaj.st