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In this paper, we propose a generic smart telemonitoring platform in which the computation power of the mobile phone is highly utilized. In this approach, compression of ECG is done in real-time by the mobile phone for the very first time. The fast and effective compression scheme, designed for the proposed telemonitoring system, outperforms most of the real-time lossless ECG compression algorithms. This mobile phone based computation platform is a promising solution for privacy issues in telemonitoring through encryptions. Moreover, the mobile phones used in this platform performs preliminary detection of abnormal biosignal in realtime. Apart from the usage of mobile phones, this platform supports background biosignal abnormality surveillance using data mining agent.