Obtaining higher-order derivatives of low-frequency signals using multirate signal processing

In this paper, a multi-rate signal processing technique is proposed for obtaining higher-order derivatives of digital signals with an improved signal-to-quantization noise ratio (SQNR). The technique consists of a classical oversampling analog-to-digital conversion (ADC) unit with a dithering process and multi-stage down sampling processing followed by a high performance digital differentiator cascaded using a decimator with a factor of two. In the cascaded multi-stage processing, each stage contains a simple half-band low-pass filter followed with decimation by two. The proposed technique uses an extremely small FIR filter size, hence requires much less memory and computational complexity in comparison with single-stage processing. Computer simulations and experimental data processing demonstrate the effectiveness of the proposed method.