  A Gravitational Wave Background (GWB) is expected in the universe from the
superposition of a large number of unresolved astrophysical sources and
phenomena in the early universe. Each component of the background (e.g., from
primordial metric perturbations, binary neutron stars, milli-second pulsars
etc.) has its own spectral shape. Many ongoing experiments aim to probe GWB at
a variety of frequency bands. In the last two decades, using data from
ground-based laser interferometric gravitational wave (GW) observatories, upper
limits on GWB were placed in the frequency range of ~50-1000 Hz, considering
one spectral shape at a time. However, one strong component can significantly
enhance the estimated strength of another component. Hence, estimation of the
amplitudes of the components with different spectral shapes should be done
jointly. Here we propose a method for "component separation" of a statistically
isotropic background, that can, for the first time, jointly estimate the
amplitudes of many components and place upper limits. The method is rather
straightforward and needs negligible amount of computation. It utilises the
linear relationship between the measurements and the amplitudes of the actual
components, alleviating the need for a sampling based method, e.g., Markov
Chain Monte Carlo (MCMC) or matched filtering, which are computationally
intensive and cumbersome in a multi-dimensional parameter space. Using this
formalism we could also study how many independent components can be separated
using a given dataset from a network of current and upcoming ground based
interferometric detectors.
