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In this paper a new shaping window is designed to force the side-lobe of OFDM transmission to decay faster than conventional raised-cosine windowing. The proposed window is a soft-window based on the characteristics of functions with vestigial symmetry, which are common in digital data transmission. By using the vestigial symmetry and enforcing several null derivatives at the extremes of the window, it is possible to control the fast out-of-band decay. Results show that by using a lower roll-off factor (10%) the proposed window can achieve the same performance of raised-cosine (100 %) with around 90% overhead savings, making it of interest for OFDM cognitive radio.