We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

The Theory of Stochastic Processes. By D. R. Cox and H. D. Miller. Pp. x, 398. 70s. (Methuen)

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An Introduction To The Theory Of Point Processes

/pdf/statistical-theory-of-communication-4wy4yg9ato.pdf

Statistical Theory of Communication

2017 25th European Signal Processing Conference (EUSIPCO)

This paper presents, on the basis of a rigorous mathematical formulation, a multicomponent sinusoidal model that allows an asymptotically exact reconstruction of nonstationary speech signals, regardless of their duration and without any limitation in the modeling of voiced, unvoiced, and transitional segments. The proposed approach is based on the application of the Hilbert transform to obtain an amplitude signal from which an AM component is extracted by filtering, so that the residue can then be iteratively processed in the same way. This technique permits a multicomponent AM-FM model to be derived in which the number of components (iterations) may be arbitrarily chosen. Additionally, the instantaneous frequencies of these components can be calculated with a given accuracy by segmentation of the phase signals. The validity of the proposed approach has been proven by some applications to both synthetic signals and natural speech. Several comparisons show how this approach almost always has a higher performance than that obtained by current best practices, and does not need the complex filter optimizations required by other techniques

Multicomponent AM–FM Representations: An Asymptotically Exact Approach

The human activity monitoring technology is one of the most important technologies for ambient assisted living, surveillance-based security, sport and fitness activities, healthcare of elderly people. The activity monitoring is performed in two steps: the acquisition of body signals and the classification of activities being performed. This paper presents a low-cost wearable wireless system specifically designed to acquire surface electromyography (sEMG) and accelerometer signals for monitoring the human activity when performing sport and fitness activities, as well as in healthcare applications. The proposed system consists of several ultralight wireless sensing nodes that are able to acquire, process and efficiently transmit the motion-related (biological and accelerometer) body signals to one or more base stations through a 2.4 GHz radio link using an ad-hoc communication protocol designed on top of the IEEE 802.15.4 physical layer. A user interface software for viewing, recording, and analysing the data was implemented on a control personal computer that is connected through a USB link to the base stations. To demonstrate the capability of the system of detecting the user’s activity, data recorded from a few subjects were used to train and test an automatic classifier for recognizing the type of exercise being performed. The system was tested on four different exercises performed by three people, the automatic classifier achieved an overall accuracy of 85.7% combining the features extracted from acceleration and sEMG signals. A low cost wireless system for the acquisition of sEMG and accelerometer signals has been presented for healthcare and fitness applications. The system consists of wearable sensing nodes that wirelessly transmit the biological and accelerometer signals to one or more base stations. The signals so acquired will be combined and processed in order to detect, monitor and recognize human activities.

/pdf/human-activity-monitoring-system-based-on-wearable-semg-and-2fgveg8ohb.pdf

Human activity monitoring system based on wearable sEMG and accelerometer wireless sensor nodes

Sport, fitness, as well as rehabilitation activities, often require the accomplishment of repetitive movements. The correctness of the exercises is often related to the capability of maintaining the required cadence and muscular force. Failure to maintain the required force, also known as muscle fatigue, is accompanied by a shift in the spectral content of the surface electromyography (EMG) signal toward lower frequencies. This paper presents a novel approach for simultaneously obtaining exercise repetition frequency and evaluating muscular fatigue, as functions of time, by only using the EMG signal. The mean frequency of the amplitude spectrum (MFA) of the EMG signal, considered as a function of time, is directly related to the dynamics of the movement performed and to the fatigue of the involved muscles. If the movement is cyclic, MFA will display the same pattern and its average will tend to decrease. These two effects have been simultaneously modeled by a two-component AM–FM model based on the Hilbert transform. The method was tested on signals recorded using a wireless system applied to healthy subjects performing dumbbell biceps curls, dumbbell lateral rises, and bodyweight squats. Experimental results show the excellent performance of the proposed technique.

Analysis of the EMG Signal During Cyclic Movements Using Multicomponent AM–FM Decomposition

Photoplethysmography (PPG) is a common and practical technique to detect human activity and other physiological parameters and is commonly implemented in wearable devices. However, the PPG signal is often severely corrupted by motion artifacts. The aim of this paper is to address the human activity recognition (HAR) task directly on the device, implementing a recurrent neural network (RNN) in a low cost, low power microcontroller, ensuring the required performance in terms of accuracy and low complexity. To reach this goal, (i) we first develop an RNN, which integrates PPG and tri-axial accelerometer data, where these data can be used to compensate motion artifacts in PPG in order to accurately detect human activity; (ii) then, we port the RNN to an embedded device, Cloud-JAM L4, based on an STM32 microcontroller, optimizing it to maintain an accuracy of over 95% while requiring modest computational power and memory resources. The experimental results show that such a system can be effectively implemented on a constrained-resource system, allowing the design of a fully autonomous wearable embedded system for human activity recognition and logging.

https://www.mdpi.com/2079-9292/10/14/1715/pdf

Recurrent Neural Network for Human Activity Recognition in Embedded Systems Using PPG and Accelerometer Data

This paper presents an efficient technique for real-time recognition of human activities by using accelerometer and photoplethysmography (PPG) data. It is based on singular value decomposition (SVD) and truncated Karhunen-Loeve transform (KLT) for feature extraction and reduction, and Bayesian classification for class recognition. Due to the nature of signals, and being the algorithm independent from the orientation of the inertial sensor, this technique is particularly suitable for implementation in smartwatches in order to both recognize the exercise being performed and improve the motion artifact (MA) removal from PPG signal for accurate heart rate (HR) estimation. In order to demonstrate the validity of this methodology, it has been successfully applied to a database of accelerometer and PPG data derived from four dynamic activities.

Giorgio Biagetti

Papers

Multicomponent AM–FM Representations: An Asymptotically Exact Approach

Human activity monitoring system based on wearable sEMG and accelerometer wireless sensor nodes

Analysis of the EMG Signal During Cyclic Movements Using Multicomponent AM–FM Decomposition

Recurrent Neural Network for Human Activity Recognition in Embedded Systems Using PPG and Accelerometer Data

Human Activity Recognition Using Accelerometer and Photoplethysmographic Signals