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This paper presents a maximum likelihood (ML) approach to mitigate the effect of narrow band interference (NBI) in a zero padded orthogonal frequency division multiplexing (ZP-OFDM) system. The NBI is assumed to be time variant and asynchronous with the frequency grid of the ZP-OFDM system. The proposed structure based technique uses the fact that the NBI signal is sparse as compared to the ZP-OFDM signal in the frequency domain. The structure is also useful in reducing the computational complexity of the proposed method. The paper also presents a data aided approach for improved NBI estimation. The suitability of the proposed method is demonstrated through simulations.