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In this letter, we present the design and realization of an integrated drop filter with optimized tapered Bragg gratings for the compensation of the optical chromatic dispersion. An apodization profile for the gratings has been determined for an optimal reduction of the group delay ripple and the enhancement of the system performance. The apodization has been carried out varying the width of the grating trenches at the two ends with a sine profile and the principle has been experimentally demonstrated. The device permits a dispersion compensation of 480 ps/nm and an error-free detection of a DQPSK signal up to 30 Gbaud.