The primary task in cognitive radio is to dynamically explore the radio spectrum and reliably detect the co-existing licensed primary transmissions across a wide-band spectrum. This paper focuses on wavelet transform (WT) based wide-band sensing techniques, which identify the edges of the multiple frequency bands simultaneously. Novel edge detection algorithms are proposed based on continuous WT (CWT) and discrete WT (DWT) techniques, applied on wide-band power spectrum. In CWT based spectrum sensing, logarithmic scaling preceded by a thresholding is performed on the CWT coefficients to enhance the small modulus maxima values at the edges, resulting in better detection probability. Since the logarithmic scaling magnifies the spurious edges, the proposed algorithm increases the false alarm probability at high noise variance. To alleviate this problem, DWT based algorithms are proposed, where DWT performs simultaneous denoising and edge detection. To achieve good detection performance at poor SNR scenario, a moving average filtering strategy is adopted at different levels of DWT based algorithms and better performance is achieved even with lower scale value of DWT, thereby reducing the computation time. Comparative studies show that the proposed algorithms outperform the existing WT based edge detection algorithms in the dynamic and frequency selective channels as well.