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Noise shaping filter in fully digital amplifier is optimized with optimal coefficients of real number suggested. To derive the coefficients, Noise Shaping Gain is suggested as an object function of the filter performance. The enhancement of performance compared to the conventional filter with integer coefficients is analyzed and simulated. The results show that the suggested filter gives much more signal to noise ratio for a given filter order.fatcat:drxv5vmktrevtlr7vux6b76koy