A Field Programmable Gate Array (FPGA) based parallel architecture for the real-time and online implementation of the bivariate extension of the empirical mode decomposition (EMD) algorithm is presented. Multivariate extensions of EMD have attracted significant attention in recent years owing to their scope in applications involving multichannel and multidimensional data processing, e.g. biomedical engineering, condition monitoring, image fusion. However, these algorithms are computationally expensive due to the empirical and data-driven nature of these methods. That has hindered the utilisation of EMD, and particularly its bivariate and multivariate extensions, in realtime applications. The proposed parallel architecture is aimed at bridging this gap through real-time computation of the bivariate EMD algorithm. The crux of the architecture is the simultaneous computation of multiple signal projections, locating their local extrema and finally the calculation of their associated complex valued envelopes for the estimation of local mean. The architecture is implemented on a Xilinx Kintex 7 FPGA, and offers significant computational improvements over the existing software based sequential implementaions of bivariate EMD.

Empirical mode decomposition (EMD) is a data driven method for nonstationary data analysis which has proven to be extremely useful in diverse applications in biomedical engineering. In its original formulation, the EMD method works collectively on a batch of data and hence is not suitable for online applications that demand continuous data processing capability in real-time. To cater for such applications, few complete field-programmable gate array (FPGA) based designs for EMD computations have emerged in recent years, yet they have found limited practical applications. The main reason could be that existing complete FPGA based architectures invariably work on integer data sets thus ignoring the sensitivity EMD to truncation errors. Moreover, these architectures mostly implement simplistic linear interpolation technique for sifting process within EMD, thereby compromising its accuracy. To that end, we develop a complete FPGA-based architecture for EMD which works on fixed point data formats thereby alleviating the main source of error in existing EMD based architectures. We also implement well established and accurate cubic spline interpolation technique in addition to giving provision to linear interpolation within the sifting process in EMD, which further improves its accuracy. Our proposed pipeline design ensures that despite implementing computationally expensive EMD related tasks, the proposed architecture exhibits lowest execution time among all existing EMD architectures. We provide examples of computation of EMD decomposition through proposed architecture for both synthetic and real world biomedical signals to demonstrate the prowess of our work.INDEX TERMS Empirical mode decomposition, FPGA, time frequency analysis.

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Multivariate or multichannel data have become ubiquitous in many modern scientific and engineering applications, e.g., biomedical engineering, owing to recent advances in sensor and computing technology. Processing these data sets is challenging owing to: i) their large size and multidimensional nature, thus requiring specialized algorithms and efficient hardware designs for on-line and real-time processing; ii) the nonstationary nature of data arising in many real life applications demanding new extensions of standard multiscale non-stationary signal processing tools. In this paper, we address the former issue by proposing a fully FPGA based hardware architecture of a popular multi-scale and multivariate signal processing algorithm, termed as multivariate empirical mode decomposition (MEMD). MEMD is a data-driven method that extends the functionality of standard empirical mode decomposition (EMD) algorithm to multichannel or multivariate data sets. Since its inception in 2010, the algorithm has found wide spread applications spanning different engineering related fields. Yet, no parallel FPGA based hardware design of the algorithm is available for its on-line and real-time processing. Our proposed architecture for MEMD uses fixed point operations and employs cubic spline interpolation within the sifting process. Finally, examples of decomposition of multivariate synthetic and real world biological signals are provided.