Spectrum sensing is one of the enabling functionalities for cognitive radio (CR) systems to operate in the spectrum white space. To protect the primary incumbent users from interference, the CR is required to detect incumbent signals at very low signal-to-noise ratio (SNR). In this paper, we present a spectrum sensing technique based on correlating spectra for detection of television (TV) broadcasting signals. The basic strategy is to correlate the periodogram of the received signal with the a priori known spectral features of the primary signal. We show that according to the Neyman-Pearson criterion, this spectra correlation-based sensing technique is asymptotically optimal at very low SNR and with a large sensing time. From the system design perspective, we analyze the effect of the spectral features on the spectrum sensing performance. Through the optimization analysis, we obtain useful insights on how to choose effective spectral features to achieve reliable sensing. Simulation results show that the proposed sensing technique can reliably detect analog and digital TV signals at SNR as low as -20 dB.