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The wavelet edge detection had a wide application in signal processing. In reference , Zhi Tian and G B Giannakis proposed a multiscale products wavelet edge detection based spectrum sensing method. In this paper, the performance of forementioned algorithm is analyzed. Then we compare this method with the edge detection using wavelet multiscale sums. From the analysis and comparison, conclusion is drawn out that multiscale products method can't detect the ultra-narrowband signals and the signals with slowly changing power spectrum density (PSD) at the same time. However, the multiscale sums method can solve this conflict effectively. Unfortunately, the multiscale sums method has some difficulty in locating the precise singularity points. For the purpose of demonstration, some simulations are given to accompany with theoretical analysis.