Developing And Comparing Numerical Methods For Computing The Inverse Fourier Transform

Computing the Fourier transform and its inverse is important in many applications of mathematics, such as frequency analysis, signal modulation, and filtering. Two methods will be derived for numerically computing the inverse Fourier transforms, and they will be compared to the standard inverse discrete Fourier transform (IDFT) method. The first computes the inverse Fourier transform through direct use of the Laguerre expansion of a function. The second employs the Riesz projections, also known as Hilbert projections, to numerically compute the inverse Fourier transform. For some smooth functions with slow decay in the frequency domain, the Laguerre and Hilbert methods will work better than the standard IDFT. Applications of the Hilbert transform method are related to the numerical solutions of nonlinear inverse scattering problems and may have implications for the associated reconstruction algorithms

Static posturography as a novel measure of the effects of aging on postural control in dogs

Aging is associated with impairment in postural control in humans. While dogs are a powerful model for the study of aging, the associations between age and postural control in this species have not yet been elucidated. The aims of this work were to establish a reliable protocol to measure center of pressure excursions in standing dogs and to determine age-related changes in postural sway. Data were obtained from 40 healthy adult dogs (Group A) and 28 senior dogs (Group B) during seven trials (within one session of data collection) of quiet standing on a pressure sensitive walkway system. Velocity, acceleration, root mean square, 95% ellipse area, range and frequency revolve were recorded as measures of postural sway. In Group A, reliability was assessed with intraclass correlation, and the effect of morphometric variables was evaluated using linear regression. By means of stepwise linear regression we determined that root mean square overall and acceleration in the craniocaudal direction were the best variables able to discriminate between Group A and Group B. The relationship between these two center-of-pressure (COP) measures and the dogs’ fractional lifespan was examined in both groups and the role of pain and proprioceptive deficits was evaluated in Group B. All measures except for frequency revolve showed good to excellent reliability. Weight, height and length were correlated with most of the measures. Fractional lifespan impacted postural control in Group B but not Group A. Joint pain and its interaction with proprioceptive deficits influence postural sway especially in the acceleration in the craniocaudal direction, while fractional lifespan was most important in the overall COP displacement. In conclusion, our study found that pressure sensitive walkway systems are a reliable tool to evaluate postural sway in dogs; and that postural sway is affected by morphometric parameters and increases with age and joint pain

CITRIC: A low-bandwidth wireless camera network platform

In this paper, we propose and demonstrate a novel wireless camera network system, called CITRIC. The core component of this system is a new hardware platform that integrates a camera, a frequency-scalable (up to 624 MHz) CPU, 16 MB FLASH, and 64 MB RAM onto a single device. The device then connects with a standard sensor network mote to form a camera mote. The design enables in-network processing of images to reduce communication requirements, which has traditionally been high in existing camera networks with centralized processing. We also propose a back-end client/server architecture to provide a user interface to the system and support further centralized processing for higher-level applications. Our camera mote enables a wider variety of distributed pattern recognition applications than traditional platforms because it provides more computing power and tighter integration of physical components while still consuming relatively little power. Furthermore, the mote easily integrates with existing low-bandwidth sensor networks because it can communicate over the IEEE 802.15.4 protocol with other sensor network platforms. We demonstrate our system on three applications: image compression, target tracking, and camera localization

Effect of sensor number and location on accelerometry-based vertical ground reaction force estimation during walking

Knee osteoarthritis is a major cause of global disability and is a major cost for the healthcare system. Lower extremity loading is a determinant of knee osteoarthritis onset and progression; however, technology that assists rehabilitative clinicians in optimizing key metrics of lower extremity loading is significantly limited. The peak vertical component of the ground reaction force (vGRF) in the first 50% of stance is highly associated with biological and patient-reported outcomes linked to knee osteoarthritis symptoms. Monitoring and maintaining typical vGRF profiles may support healthy gait biomechanics and joint tissue loading to prevent the onset and progression of knee osteoarthritis. Yet, the optimal number of sensors and sensor placements for predicting accurate vGRF from accelerometry remains unknown. Our goals were to: 1) determine how many sensors and what sensor locations yielded the most accurate vGRF loading peak estimates during walking; and 2) characterize how prescribing different loading conditions affected vGRF loading peak estimates. We asked 20 young adult participants to wear 5 accelerometers on their waist, shanks, and feet and walk on a force-instrumented treadmill during control and targeted biofeedback conditions prompting 5% underloading and overloading vGRFs. We trained and tested machine learning models to estimate vGRF from the various sensor accelerometer inputs and identified which combinations were most accurate. We found that a neural network using one accelerometer at the waist yielded the most accurate loading peak vGRF estimates during walking, with average errors of 4.4% body weight. The waist-only configuration was able to distinguish between control and overloading conditions prescribed using biofeedback, matching measured vGRF outcomes. Including foot or shank acceleration signals in the model reduced accuracy, particularly for the overloading condition. Our results suggest that a system designed to monitor changes in walking vGRF or to deploy targeted biofeedback may only need a single accelerometer located at the waist for healthy participants