  We develop new techniques to deconvolve the radial structure of the X-ray
emission region in the bright low/hard state of the black hole Cygnus X-1 using
both spectral and timing data in the 3-35~keV range. The spectrum at these
energies is dominated by Comptonisation rather than the disc, but there is a
complex pattern in the time lags between different energy bands and differences
in the normalisation and shape in the power spectra of these bands, which
clearly shows that the Comptonisation is not produced from a single,
homogeneous region. We use a physically based model of density fluctuations
propagating through a spectrally inhomogeneous flow, setting the spectral
components by jointly fitting to the time-averaged and Fourier resolved
spectra. The predicted variability in any band is modelled analytically in
Fourier space so it can be fit directly to the observed power spectra and lags.
We find that the best fit model picks out three distinct radii in the flow,
each with a distinct Compton spectrum. The variability and luminosity produced
at these radii is enhanced, while propagation of fluctuations from larger radii
is suppressed. We associate these radii with the disc truncation, the inner
edge of the flow, and (more speculatively) the jet launch radius. These
distinct radii are most evident where the source is close to a transition
between the low/hard and high/soft states. We suggest that the smoother power
spectra seen at lower luminosities imply that the source structure is simpler
away from the transition.
