A new spectrum sensing method based on the joint use of local polynomial time frequency transform (LPTFT) and Hough transform (HT) is proposed. Theoretical analysis of the detection probability of the proposed method and the associated statistical models are provided. The proposed method is used for sensing the wireless microphone (WM) signals in cognitive radio (CR) and the experimental results based on Monte Carlo realization indicate that the proposed method is able to detect the WM signals in heavy noise environments, i.e., in the range of negative SNRs, and provides a much better detection performance than other methods such as energy detection (ED), short time Fourier transform-HT (SHT) and pseudo Wigner-Ville distribution-HT (PWHT).