Ervin Sejdić

Fractional Fourier transform as a signal processing tool: An overview of recent developments

Fractional Fourier transform (FRFT) is a generalization of the Fourier transform, rediscovered many times over the past 100 years. In this paper, we provide an overview of recent contributions pertaining to the FRFT. Specifically, the paper is geared toward signal processing practitioners by emphasizing the practical digital realizations and applications of the FRFT. It discusses three major topics. First, the manuscripts relates the FRFT to other mathematical transforms. Second, it discusses various approaches for practical realizations of the FRFT. Third, we overview the practical applications of the FRFT. From these discussions, we can clearly state that the FRFT is closely related to other mathematical transforms, such as time-frequency and linear canonical transforms. Nevertheless, we still feel that major contributions are expected in the field of the digital realizations and its applications, especially, since many digital realizations of the FRFT still lack properties of the continuous FRFT. Overall, the FRFT is a valuable signal processing tool. Its practical applications are expected to grow significantly in years to come, given that the FRFT offers many advantages over the traditional Fourier analysis.

A Comprehensive Assessment of Gait Accelerometry Signals in Time, Frequency and Time-Frequency Domains

Gait accelerometry is a promising tool to assess human walking and reveal deteriorating gait characteristics in patients and can be a rich source of clinically relevant information about functional declines in older adults. Therefore, in this paper, we present a comprehensive set of signal features that may be used to extract clinically valuable information from gait accelerometry signals. To achieve our goal, we collected tri-axial gait accelerometry signals from 35 adults 65 years of age and older. Fourteen subjects were healthy controls, 10 participants were diagnosed with Parkinsons disease, and 11 participants were diagnosed with peripheral neuropathy. The data were collected while the participants walked on a treadmill at a preferred walking speed. Accelerometer signal features in time, frequency and time-frequency domains were extracted. The results of our analysis showed that some of the extracted features were able to differentiate between healthy and clinical populations. Signal features in all three domains were able to emphasize variability among different groups, and also revealed valuable information about variability of the signals between anterior-posterior, mediolateral, and vertical directions within subjects. The current results imply that the proposed signal features can be valuable tools for the analysis of gait accelerometry data and should be utilized in future studies.

An empirical examination of detrended fluctuation analysis for gait data.

Stride interval series exhibit statistical persistence, and detrended fluctuation analysis (DFA) is a routinely employed technique for describing this behavior. However, the implementation of DFA to gait data varies considerably between studies. We empirically examine two practical aspects of DFA which significantly affect the analysis outcome: the box size range and the stride interval series length. We conduct an analysis of their effect using stride intervals from 16 able-bodied adults, for overground walking, treadmill walking while holding a handrail, and treadmill walking without using a handrail. Our goal is to provide general guidelines for these two choices, with the aim of standardizing the application of DFA and facilitating inter-study comparisons. Based on the results of our analysis, we propose the use of box sizes from 16 to N/9, where N is the number of stride intervals. Moreover, for differentiating between normal and pathological walking with reasonable accuracy, we recommend a minimum of 600 stride intervals.

A window width optimized S-transform

Energy concentration of the S-transform in the time-frequency domain has been addressed in this paper by optimizing the width of the window function used. A new scheme is developed and referred to as a window width optimized S-transform. Two optimization schemes have been proposed, one for a constant window width, the other for time-varying window width. The former is intended for signals with constant or slowly varying frequencies, while the latter can deal with signals with fast changing frequency components. The proposed scheme has been evaluated using a set of test signals. The results have indicated that the new scheme can provide much improved energy concentration in the time-frequency domain in comparison with the standard S-transform. It is also shown using the test signals that the proposed scheme can lead to higher energy concentration in comparison with other standard linear techniques, such as short-time Fourier transform and its adaptive forms. Finally, the method has been demonstrated on engine knock signal analysis to show its effectiveness.

Compressive sampling of swallowing accelerometry signals using time-frequency dictionaries based on modulated discrete prolate spheroidal sequences

Monitoring physiological functions such as swallowing often generates large volumes of samples to be stored and processed, which can introduce computational constraints especially if remote monitoring is desired. In this article, we propose a compressive sensing (CS) algorithm to alleviate some of these issues while acquiring dual-axis swallowing accelerometry signals. The proposed CS approach uses a time-frequency dictionary where the members are modulated discrete prolate spheroidal sequences (MDPSS). These waveforms are obtained by modulation and variation of discrete prolate spheroidal sequences (DPSS) in order to reflect the time-varying nature of swallowing acclerometry signals. While the modulated bases permit one to represent the signal behavior accurately, the matching pursuit algorithm is adopted to iteratively decompose the signals into an expansion of the dictionary bases. To test the accuracy of the proposed scheme, we carried out several numerical experiments with synthetic test signals and dual-axis swallowing accelerometry signals. In both cases, the proposed CS approach based on the MDPSS yields more accurate representations than the CS approach based on DPSS. Specifically, we show that dual-axis swallowing accelerometry signals can be accurately reconstructed even when the sampling rate is reduced to half of the Nyquist rate. The results clearly indicate that the MDPSS are suitable bases for swallowing accelerometry signals.

Measures of dynamic stability: Detecting differences between walking overground and on a compliant surface

Numerous measures of dynamic stability have been proposed to gauge fall risk in the elderly, including stride interval variability and variability of the center of mass. However, these measures have been deemed inadequate because they do not take into account temporal information. Therefore, research on the measurement of dynamic stability has turned to other analysis methods such as stride interval dynamics and the maximum Lyapunov exponent. Stride interval dynamics reflect the statistical persistence of an individuals stride interval time series and the Lyapunov exponent quantifies local dynamic stability - the sensitivity of the system to infinitesimal perturbations. In this study, we compare the ability of these measurement tools to detect changes between overground and compliant-surface walking, a condition known to affect stability, to determine their aptness as measures of dynamic stability. Fourteen able-bodied participants completed three 15 min walks, two overground and one on a compliant surface. Our results show that the Lyapunov exponent may be more sensitive to gait changes than stride interval dynamics and gait variability measures.

Segmentation of Dual-Axis Swallowing Accelerometry Signals in Healthy Subjects With Analysis of Anthropometric Effects on Duration of Swallowing Activities

Dysphagia (swallowing difficulty) is a serious and debilitating condition that often accompanies stroke, acquired brain injury, and neurodegenerative illnesses. Individuals with dysphagia are prone to aspiration (the entry of foreign material into the airway), which directly increases the risk of serious respiratory consequences such as pneumonia. Swallowing accelerometry is a promising noninvasive tool for the detection of aspiration and the evaluation of swallowing. In this paper, dual-axis accelerometry was implemented since the motion of the hyolaryngeal complex occurs in both anterior-posterior and superior-inferior directions during swallowing. Dual-axis cervical accelerometry signals were acquired from 408 healthy subjects during dry, wet, and wet chin tuck swallowing tasks. The proposed segmentation algorithm is based on the idea of sequential fuzzy partitioning of the signal and is well suited for long signals with nonstationary variance. The algorithm was validated with simulated signals with known swallowing locations and a subset of 295 real swallows manually segmented by an experienced speech language pathologist. In both cases, the algorithm extracted individual swallows with over 90% accuracy. The time duration analysis was carried out with respect to gender, body mass index (BMI), and age. Demographic and anthropometric variables influenced the duration of these segmented signals. Male participants exhibited longer swallows than female participants (p=0.05). Older participants and participants with higher BMIs exhibited swallows with significantly longer (p=0.05) duration than younger participants and those with lower BMIs, respectively.

The Effects of Rhythmic Sensory Cues on the Temporal Dynamics of Human Gait

Walking is a complex, rhythmic task performed by the locomotor system. However, natural gait rhythms can be influenced by metronomic auditory stimuli, a phenomenon of particular interest in neurological rehabilitation. In this paper, we examined the effects of aural, visual and tactile rhythmic cues on the temporal dynamics associated with human gait. Data were collected from fifteen healthy adults in two sessions. Each session consisted of five 15-minute trials. In the first trial of each session, participants walked at their preferred walking speed. In subsequent trials, participants were asked to walk to a metronomic beat, provided through visually, aurally, tactile or all three cues (simultaneously and in sync), the pace of which was set to the preferred walking speed of the first trial. Using the collected data, we extracted several parameters including: gait speed, mean stride interval, stride interval variability, scaling exponent and maximum Lyapunov exponent. The extracted parameters showed that rhythmic sensory cues affect the temporal dynamics of human gait. The auditory rhythmic cue had the greatest influence on the gait parameters, while the visual cue had no statistically significant effect on the scaling exponent. These results demonstrate that visual rhythmic cues could be considered as an alternative cueing modality in rehabilitation without concern of adversely altering the statistical persistence of walking.

Carbon Nanotube Chemiresistor for Wireless pH Sensing

The ability to accurately measure real-time pH fluctuations in-vivo could be highly advantageous. Early detection and potential prevention of bacteria colonization of surgical implants can be accomplished by monitoring associated acidosis. However, conventional glass membrane or ion-selective field-effect transistor (ISFET) pH sensing technologies both require a reference electrode which may suffer from leakage of electrolytes and potential contamination. Herein, we describe a solid-state sensor based on oxidized single-walled carbon nanotubes (ox-SWNTs) functionalized with the conductive polymer poly(1-aminoanthracene) (PAA). This device had a Nernstian response over a wide pH range (2–12) and retained sensitivity over 120 days. The sensor was also attached to a passively-powered radio-frequency identification (RFID) tag which transmits pH data through simulated skin. This battery-less, reference electrode free, wirelessly transmitting sensor platform shows potential for biomedical applications as an implantable sensor, adjacent to surgical implants detecting for infection.

A Brain-Computer Interface Based on Bilateral Transcranial Doppler Ultrasound

In this study, we investigate the feasibility of a BCI based on transcranial Doppler ultrasound (TCD), a medical imaging technique used to monitor cerebral blood flow velocity. We classified the cerebral blood flow velocity changes associated with two mental tasks - a word generation task, and a mental rotation task. Cerebral blood flow velocity was measured simultaneously within the left and right middle cerebral arteries while nine able-bodied adults alternated between mental activity (i.e. word generation or mental rotation) and relaxation. Using linear discriminant analysis and a set of time-domain features, word generation and mental rotation were classified with respective average accuracies of 82.9%10.5 and 85.7%10.0 across all participants. Accuracies for all participants significantly exceeded chance. These results indicate that TCD is a promising measurement modality for BCI research.