Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

Relative entropy rate based model selection for linear hybrid system filters of uncertain nonlinear systems

Hybrid system representations have been exploited in a number of challenging modelling situations, including situations where the original nonlinear dynamics are too complex (or too imprecisely known) to be directly filtered. Unfortunately, the question of how to best design suitable hybrid system models has not yet been fully addressed, particularly in the situations involving model uncertainty. This paper proposes a novel joint state-measurement relative entropy rate based approach for design of hybrid system filters in the presence of (parameterised) model uncertainty. We also present a design approach suitable for suboptimal hybrid system filters. The benefits of our proposed approaches are illustrated through design examples and simulation studies.

The post-illumination pupil response of melanopsin expressing intrinsically photosensitive retinal ganglion cells in diabetes

Purpose: This study investigates the clinical utility of the melanopsin expressing intrinsically photosensitive retinal ganglion cell (ipRGC) controlled post-illumination pupil response (PIPR) as a novel technique for documenting inner retinal function in patients with Type II diabetes without diabetic retinopathy. Methods: The post-illumination pupil response (PIPR) was measured in seven patients with Type II diabetes, normal retinal nerve fiber thickness and no diabetic retinopathy. A 488 nm and 610 nm, 7.15º diameter stimulus was presented in Maxwellian view to the right eye and the left consensual pupil light reflex was recorded. Results: The group data for the blue PIPR (488 nm) identified a trend of reduced ipRGC function in patients with diabetes with no retinopathy. The transient pupil constriction was lower on average in the diabetic group. The relationship between duration of diabetes and the blue PIPR amplitude was linear, suggesting that ipRGC function decreases with increasing diabetes duration. Conclusion: This is the first report to show that the ipRGC controlled post-illumination pupil response may have clinical applications as a non-invasive technique for determining progression of inner neuroretinal changes in patients with diabetes before they are ophthalmoscopically or anatomically evident. The lower transient pupil constriction amplitude indicates that outer retinal photoreceptor inputs to the pupil light reflex may also be affected in diabetes.

Temporal summation of intrinsically photosensitive retinal ganglion cell (ipRGC) contributions to the human pupil.

Purpose: IpRGCs mediate non-image forming functions including photoentrainment and the pupil light reflex (PLR). Temporal summation increases visual sensitivity and decreases temporal resolution for image forming vision, but the summation properties of nonimage forming vision are unknown. We investigated the temporal summation of inner (ipRGC) and outer (rod/cone) retinal inputs to the PLR. Method: The consensual PLR of the left eye was measured in six participants with normal vision using a Maxwellian view infrared pupillometer. Temporal summation was investigated using a double-pulse protocol (100 ms stimulus pairs; 0–1024 ms inter-stimulus interval, ISI) presented to the dilated fellow right eye (Tropicamide 1%). Stimulus lights (blue λmax = 460 nm; red λmax = 638 nm) biased activity to inneror outer retinal inputs to non-image forming vision. Temporal summation was measured suprathreshold (15.2 log photons.cm−2.s−1 at the cornea) and subthreshold (11.4 log photons.cm−2.s−1 at the cornea). Results: RM-ANOVAs showed the suprathreshold and subthreshold 6 second post illumination pupil response (PIPR: expressed as percentage baseline diameter) did not significantly vary for red or blue stimuli (p > .05). The PIPR for a subthreshold red 16 ms double-pulse control condition did not significantly differ with ISI (p > .05). The maximum constriction amplitude for red and blue 100 ms double- pulse stimuli did not significantly vary with ISI (p > .05). Conclusion: The non-significant changes in suprathreshold PIPR and subthreshold maximum pupil constriction indicate that inner retinal ipRGC inputs and outer retinal photoreceptor inputs to the PLR do not show temporal summation. The results suggest a fundamental difference between the temporal summation characteristics of image forming and non-image forming vision.

Probing second harmonic components of pH-sensitive Redox processes in a mesoporous TiO2-Nafion film electrode with Fourier-transformed large-amplitude sinusoidally modulated voltammetry

Electrochemical processes in mesoporous TiO2-Nafion thin films deposited on indium tin oxide (ITO) electrodes are inherently complex and affected by capacitance, Ohmic iR-drop, RC-time constant phenomena, and by potential and pH-dependent conductivity. In this study, large-amplitude sinusoidally modulated voltammetry (LASMV) is employed to provide access to almost purely Faradaic-based current data from second harmonic components, as well as capacitance and potential domain information from the fundamental harmonic for mesoporous TiO2-Nafion film electrodes. The LASMV response has been investigated with and without an immobilized one-electron redox system, ferrocenylmethyltrimethylammonium+. Results clearly demonstrate that the electron transfer associated with the immobilized ferrocene derivative follows two independent pathways i) electron hopping within the Nafion network and ii) conduction through the TiO2 backbone. The pH effect on the voltammetric response for the TiO2 reduction pathway (ii) can be clearly identified in the 2nd harmonic LASMV response with the diffusion controlled ferrocene response (i) acting as a pH independent reference. Application of second harmonic data derived from LASMV measurement, because of the minimal contribution from capacitance currents, may lead to reference-free pH sensing with systems like that found for ferrocene derivatives.

Assessing rod, cone and melanopsin contributions to human pupil flicker responses

Purpose: To determine the relative contributions of rods, cones and melanopsin to pupil responses in humans using temporal sinusoidal stimulation for light levels spanning the low mesopic to photopic range. Methods: A four-primary Ganzfeld photostimulator controlled flicker stimulations at seven light levels (-2.7 to 2 log cd/m2) and five frequencies (0.5 to 8Hz). Pupil diameter was measured using a high-resolution eyetracker. Three kinds of sinusoidal photoreceptor modulations were generated using silent substitution: 1) rod modulation, 2) cone modulation, and 3) combined rod and cone modulation in phase (Experiment 1) or phase shifted (Experiment 2) from a fixed rod phase. The melanopsin excitation was computed for each condition. A vector sum model was used to estimate the relative contribution of rods, cones and melanopsin to the pupil response. Results: From Experiment 1, the pupil frequency response peaked at 1Hz at two mesopic light levels for the three modulation conditions. Analyzing the rod-cone phase difference for the combined modulations (Experiment 2) identified a V-shaped response amplitude with a minimum between 135° and 180°. The pupil response phases increased as cone modulation phase increased. The pupil amplitude increased with increasing light level for cone and combined in-phase rod and cone modulation, but not for the rod modulation. Conclusions: These results demonstrate that cone- and rod-pathway contributions are more predominant than melanopsin contribution to the phasic pupil response. The combined rod, cone and melanopsin inputs to the phasic state of the pupil light reflex follow linear summation.

Temporal characteristics of melanopsin inputs to the human pupil light reflex

Rods, cones and melanopsin containing intrinsically photosensitive retinal ganglion cells (ipRGCs) operate in concert to regulate pupil diameter. The temporal properties of intrinsic ipRGC signalling are distinct to those of rods and cones, including longer latencies and sustained signalling after light offset. We examined whether the melanopsin mediated post-illumination pupil response (PIPR) and pupil constriction were dependent upon the inter-stimulus interval (ISI) between successive light pulses and the temporal frequency of sinusoidal light stimuli. Melanopsin excitation was altered by variation of stimulus wavelength (464 nm and 638 nm lights) and irradiance (11.4 and 15.2 log photons cm(-2) s(-1)). We found that 6s PIPR amplitude was independent of ISI and temporal frequency for all melanopsin excitation levels, indicating complete summation. In contrast to the PIPR, the maximum pupil constriction increased with increasing ISI with high and low melanopsin excitation, but time to minimum diameter was slower with high melanopsin excitation only. This melanopsin response to briefly presented pulses (16 and 100 ms) slows the temporal response of the maximum pupil constriction. We also demonstrate that high melanopsin excitation attenuates the phasic peak-trough pupil amplitude compared to conditions with low melanopsin excitation, indicating an interaction between inner and outer retinal inputs to the pupil light reflex. We infer that outer retina summation is important for rapidly controlling pupil diameter in response to short timescale fluctuations in illumination and may occur at two potential sites, one that is presynaptic to extrinsic photoreceptor input to ipRGCs, or another within the pupil control pathway if ipRGCs have differential temporal tuning to extrinsic and intrinsic signalling.

Turbulence and Mixing in the Environment: Multi-Device Study in a Sub-tropical Estuary

In an estuary, mixing and dispersion result from a combination of large-scale advection and smallscale turbulence, which are complex to estimate. The predictions of scalar transport and mixing are often inferred and rarely accurate, due to inadequate understanding of the contributions of these difference scales to estuarine recirculation. A multi-device field study was conducted in a small sub-tropical estuary under neap tide conditions with near-zero fresh water discharge for about 48 hours. During the study, acoustic Doppler velocimeters (ADV) were sampled at high frequency (50 Hz), while an acoustic Doppler current profiler (ADCP) and global positioning system (GPS) tracked drifters were used to obtain some lower frequency spatial distribution of the flow parameters within the estuary. The velocity measurements were complemented with some continuous measurement of water depth, conductivity, temperature and some other physiochemical parameters. Thorough quality control was carried out by implementation of relevant error removal filters on the individual data set to intercept spurious data. A triple decomposition (TD) technique was introduced to access the contributions of tides, resonance and ‘true’ turbulence in the flow field. The time series of mean flow measurements for both the ADCP and drifter were consistent with those of the mean ADV data when sampled within a similar spatial domain. The tidal scale fluctuation of velocity and water level were used to examine the response of the estuary to tidal inertial current. The channel exhibited a mixed type wave with a typical phase-lag between 0.035π– 0.116π. A striking feature of the ADV velocity data was the slow fluctuations, which exhibited large amplitudes of up to 50% of the tidal amplitude, particularly in slack waters. Such slow fluctuations were simultaneously observed in a number of physiochemical properties of the channel. The ensuing turbulence field showed some degree of anisotropy. For all ADV units, the horizontal turbulence ratio ranged between 0.4 and 0.9, and decreased towards the bed, while the vertical turbulence ratio was on average unity at z = 0.32 m and approximately 0.5 for the upper ADV (z = 0.55 m). The result of the statistical analysis suggested that the ebb phase turbulence field was dominated by eddies that evolved from ejection type process, while that of the flood phase contained mixed eddies with significant amount related to sweep type process. Over 65% of the skewness values fell within the range expected of a finite Gaussian distribution and the bulk of the excess kurtosis values (over 70%) fell within the range of -0.5 and +2. The TD technique described herein allowed the characterisation of a broader temporal scale of fluctuations of the high frequency data sampled within the durations of a few tidal cycles. The study provides characterisation of the ranges of fluctuation required for an accurate modelling of shallow water dispersion and mixing in a sub-tropical estuary.

The Post-Illumination Pupil Response (PIPR)

Purpose The post-illumination pupil response (PIPR) has been quantified using four metrics, but the spectral sensitivity of only one is known; here we determine the other three. To optimize the human PIPR measurement, we determine the protocol producing the largest PIPR, the duration of the PIPR, and the metric(s) with the lowest coefficient of variation. Methods The consensual pupil light reflex (PLR) was measured with a Maxwellian view pupillometer. - Experiment 1: Spectral sensitivity of four PIPR metrics [plateau, 6 s, area under curve (AUC) early and late recovery] was determined from a criterion PIPR to a 1s pulse and fitted with Vitamin A1 nomogram (λmax = 482nm). - Experiment 2: The PLR was measured as a function of three stimulus durations (1s, 10s, 30s), five irradiances spanning low to high melanopsin excitation levels (retinal irradiance: 9.8 to 14.8 log quanta.cm-2.s-1), and two wavelengths, one with high (465nm) and one with low (637nm) melanopsin excitation. Intra and inter-individual coefficients of variation (CV) were calculated. Results The melanopsin (opn4) photopigment nomogram adequately describes the spectral sensitivity of all four PIPR metrics. The PIPR amplitude was largest with 1s short wavelength pulses (≥ 12.8 log quanta.cm-2.s-1). The plateau and 6s PIPR showed the least intra and inter-individual CV (≤ 0.2). The maximum duration of the sustained PIPR was 83.0±48.0s (mean±SD) for 1s pulses and 180.1±106.2s for 30s pulses (465nm; 14.8 log quanta.cm-2.s-1). Conclusions All current PIPR metrics provide a direct measure of the intrinsic melanopsin photoresponse. To measure progressive changes in melanopsin function in disease, we recommend that the PIPR be measured using short duration pulses (e.g., ≤ 1s) with high melanopsin excitation and analyzed with plateau and/or 6s metrics. Our PIPR duration data provide a baseline for the selection of inter-stimulus intervals between consecutive pupil testing sequences.

Melanopsin mediated post-illumination pupil response in early age-related macular degeneration

Purpose To determine whether melanopsin expressing intrinsically photosensitive Retinal Ganglion Cell (ipRGC) inputs to the pupil light reflex (PLR) are affected in early age-related macular degeneration (AMD). Methods The PLR was measured in 40 participants (20 early AMD and 20 age-matched controls) using a custom-built Maxwellian-view pupillometer. Sinusoidal stimuli (0.5 Hz, 11.9 s duration, 35.6° diameter) were presented to the study eye and the consensual pupil response was measured for stimuli with high melanopsin excitation (464nm; blue) and with low melanopsin excitation (638 nm; red) that biased activation to the outer retina. Two melanopsin PLR metrics were quantified: the Phase Amplitude Percentage (PAP) during the sinusoidal stimulus presentation and the Post-Illumination Pupil Response (PIPR). The PLR during stimulus presentation was analyzed using latency to constriction, transient pupil response and maximum pupil constriction metrics. Diagnostic accuracy was evaluated using receiver operating characteristic (ROC) curves. Results The blue PIPR was significantly less sustained in the early AMD group (p<0.001). The red PIPR was not significantly different between groups (p>0.05). The PAP and blue stimulus constriction amplitude were significantly lower in the early AMD group (p < 0.05). There was no significant difference between groups in the latency or transient amplitude for both stimuli (p>0.05). ROC analysis showed excellent diagnostic accuracy for the blue PIPR metrics (AUC>0.9). Conclusions This is the initial report that the melanopsin controlled PIPR is dysfunctional in early AMD. The non-invasive, objective measurement of the ipRGC controlled PIPR has excellent diagnostic accuracy for early AMD.

The post-illumination pupil response of melanopsin expressing retinal ganglion cells

Purpose The post-illumination pupil response (PIPR) has been quantified in the literature by four metrics. The spectral sensitivity of only one metric is known and this study quantifies the other three. To optimize the measurement of the PIPR in humans, we also determine the stimulus protocol producing the largest PIPR, the duration of the PIPR, and the metric(s) with the lowest coefficient of variation. Methods The consensual pupil light reflex (PLR) was measured with a Maxwellian view pupillometer (35.6° diameter stimulus). - Experiment 1: Spectral sensitivity of four PIPR metrics [plateau, 6 s, area under curve (AUC) early and late recovery] was determined from a criterion PIPR (n = 2 participants) to a 1 s pulse at five wavelengths (409-592nm) and fitted with Vitamin A nomogram (ƛmax = 482 nm). - Experiment 2: The PLR was measured in five healthy participants [29 to 42 years (mean = 32.6 years)] as a function of three stimulus durations (1 s, 10 s, 30 s), five irradiances spanning low to high melanopsin excitation levels (retinal irradiance: 9.8 to 14.8 log quanta.cm-2.s-1), and two wavelengths, one with high (465 nm) and one with low (637 nm) melanopsin excitation. Intra and inter-individual coefficients of variation (CV) were calculated. Results The melanopsin (opn4) photopigment nomogram adequately described the spectral sensitivity derived from all four PIPR metrics. The largest PIPR amplitude was observed with 1 s short wavelength pulses (retinal irradiance ≥ 12.8 log quanta.cm-2.s-1). Of the 4 PIPR metrics, the plateau and 6 s PIPR showed the least intra and inter-individual CV (≤ 0.2). The maximum duration of the sustained PIPR was 83.4 ± 48.0 s (mean ± SD) for 1 s pulses and 180.1 ± 106.2 s for 30 s pulses (465 nm; 14.8 log quanta.cm-2.s-1). Conclusions All current PIPR metrics provide a direct measure of intrinsic melanopsin retinal ganglion cell function. To measure progressive changes in melanopsin function in disease, we recommend that the intrinsic melanopsin response should be measured using a 1 s pulse with high melanopsin excitation and the PIPR should be analyzed with the plateau and/or 6 s metrics. That the PIPR can have a sustained constriction for as long as 3 minutes, our PIPR duration data provide a baseline for the selection of inter-stimulus intervals between consecutive pupil testing sequences.

Raman spectroscopy of some complex arsenate minerals—implications for soil remediation

The application of spectroscopy to the study of contaminants in soils is important. Among the many contaminants is arsenic, which is highly labile and may leach to non-contaminated areas. Minerals of arsenate may form depending upon the availability of specific cations for example calcium and iron. Such minerals include carminite, pharmacosiderite and talmessite. Each of these arsenate minerals can be identified by its characteristic Raman spectrum enabling identification.