This paper presents new spectrum sensing algorithms based on the cumulative power spectral density (CPSD). The proposed detectors examine the CPSD of the received signal to make a decision on the absence/presence of the primary user (PU) signal. Those detectors require the whiteness of the noise in the band of interest. The false alarm and detection probabilities are derived analytically and simulated under Gaussian and Rayleigh fading channels. Our proposed detectors present better performance than the energy (ED) or the cyclostationary detectors (CSD). Moreover, in the presence of noise uncertainty (NU), they are shown to provide more robustness than ED, with less performance loss. In order to neglect the NU, we modified our algorithms to be independent from the noise variance.