Acquisition and Processing of Chromatic Derivatives using FPGA-based Digital Hardware

Chromatic derivatives (CDs) and associated chromatic approximations (CAs) provide a numerically robust and powerful framework for digital processing of continuous-time/space signals, using not only the discrete signal amplitudes, but also higher order derivatives. Acquisition of CDs has so far been limited to software implementations. This paper presents field-programmable gate array (FPGA)-based digital hardware architectures suitable for the real-time acquisition of CDs, thus enabling CDs to be used for practical signal processing algorithm development in embedded systems. With 24 bits of fixed-point precision, the proposed hardware architectures provide approximate 116 dB accuracy in the frequency responses of FIR filters capturing the CDs, and 76.85 dB and 75.09 dB accuracy in signal reconstruction with synthetic and real audio signals using CDs up to order 28 degrees. The designs have been verified on an AMD Kintex UltraScale KCU105 FGPA device using bit-true cycle-accurate hardware co-simulation.