We calculated the gravitational wave background from binary systems and rotating neutron stars using Pablo A. Rosado’s recipes of calculating spectral functions with the latest models and cosmological parameters. The overlap functions in Rosado’s works can characterize the resolvability and continuity of the background. Compare the predicted unresolvable and continuous gravitational wave backgrounds to the sensitivity curves of gravitational wave detectors, we can know from which target the background can be detected by the current and planned detectors, and whether the detector would be contaminate by the unresolvable signals. Our results show that the ground-based detectors are free from the unresolvable backgrounds both from binary systems and rotating neutron stars.