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A new hybrid predictive coding scheme for lossy data compression is introduced and studied here. The proposed technique attempts to improve the compression performance of a conventional adaptive predictive coder through three levels of prediction. The first level estimates and removes a time-varying mean signal. The second level uses DFT and IDFT to estimate and remove the predictable high frequency subband component of the signal, whereas the third level performs the adaptive predictive coding of the smoothed signal. The resultant residual is then quantized using an adaptive quantizer with 3 and 5 levels. Experimental results based on a group of test signals seem to indicate that the proposed hybrid scheme can improve the lossy compression achievable using a conventional adaptive predictive coder.