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In this paper we present a method to mitigate the effects of a narrowband interference present in an adjacent subchannel of a filter bank based multicarrier (FBMC) system. For this purpose, we use the spectral shaping capabilities of a low-complexity subchannel equalizer for filter banks. With this method, over 20 dB stronger narrowband interference (NBI) power can be tolerated as compared to a system without interference mitigation. These findings are relevant when improving the throughput / spectral efficiency of an FBMC system in environments with narrowband interference.