Embedded AM-FM Signal Decomposition Algorithm for Continuous Human Activity Monitoring

AM-FM decomposition techniques have been successfully used for extracting significative features from a large variety of signals, helping realtime signal monitoring and pattern recognition, since they represent signals as a simultaneous composition of amplitude modulation and frequency modulation, where the carriers, amplitude envelopes, and the instantaneous frequencies are the features to be estimated. Human activities often involve repetitive movements, such as in running or cycling, where sinusoidal AM-FM decompositions of signals have already demonstrated to be useful to extract compact features to aid monitoring, classification, or detection. In this work we thus present the challenges and results of implementing the iterated coherent Hilbert decomposition (ICHD), a particularly effective algorithm to obtain an AM-FM decomposition, within a resource-constrained and low-power ARM Cortex-M4 microcontroller that is present in a wearable sensor we developed. We apply ICHD to the gyroscope data acquired from an inertial measurement unit (IMU) that is present in the sensor. Optimizing the implementation allowed us to achieve real-time performance using less then 16 % of the available CPU time, while consuming only about 5.4 mW of power, which results in a run-time of over 7 days using a small 250 mAh rechargeable cell

Asymptotically exact AM-FM decomposition based on iterated Hilbert transform

This paper presents a multicomponent sinusoidal model of speech signals, obtained through a rigorous mathematical formulation that ensures an asymptotically exact reconstruction of these nonstationary signals, despite the presence of transients, voiced segments, or unvoiced segments. This result has been obtained by means of the iterated use of the Hilbert transform, and the convergence properties of the proposed method have been both analytically investigated and empirically tested. Finally, an adaptive segmentation algorithm used to accurately compute instantaneous frequencies from unwrapped phases, suited to complete the proposed AM-FM model, is presented