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In this paper, a framework for obtaining the higher order derivative of digital signals with an improved signal-to-quantization-noise ratio (SQNR) is developed. The framework consists of an oversampling analog-to-digital conversion unit with a dithering process and a higher order finite-impulse response (FIR) digital differentiator followed by a decimator. A simple and effective recursion is derived for designing the higher order FIR digital differentiator. In addition, the SQNR is analyzed. Computer simulations validate the proposed framework, the differentiator design method, and the results of the improved SQNR.