Multirate Processing Technique for Obtaining Integer and Fractional-Order Derivatives of Low-Frequency Signals

This paper proposes a multirate processing technique for obtaining integer and fractional derivatives of digital signals with an improved signal-to-quantization noise ratio. The technique consists of an oversampling analog-to-digital conversion unit with a dithering process and multistage down sampling process followed by an half-band finite impulse response (FIR) differentiator with high performance cascaded using a decimator with a factor of two. In the cascaded multistage processing, each stage contains a simple half-band low-pass FIR filter followed with decimation by two. The proposed technique uses an extremely small size for each half-band low-pass filter, hence requiring much less memory and computational complexity in comparison with the single-stage process. Computer simulations and experimental data processing demonstrate the effectiveness of the proposed method.