Four linked experiments were run in order to understand the relationship between frequency judgment and recognition discrimination tasks. The purpose of these studies was to contrast the common-path model and recursive reminding hypothesis as explanations for the underlying principles that drive these tasks. Item-attribute variables such as printed frequency, connectivity, and set size, and an episodic variable, study frequency were manipulated. Memory for recent episodes was evaluated using recognition and frequency judgment tasks. Although all of the variables, with the exception of set size, had significant effects in both tasks, an analysis of effect sizes revealed differences between the tasks in relation to the variables. Specifically, the item-attribute variables had larger effects in recognition than in JOF, and the effect size for study frequency was greater in the JOF task compared to recognition. The reliability of these differences was statistically established by a repeated measures analysis run on the correlations between each subject's mean and the variables. Although the effect size pattern is consistent with the reminding hypothesis, the effects of connectivity and printed frequency in the JOF task are not as they represent familiarity measures. Thus, this finding indicates that familiarity must be involved in making frequency judgments, making the reminding hypothesis inadequate as an explanation as it does not take into account the effect of item-attribute variables and their contribution to familiarity with its subsequent effect on frequency estimates. Therefore, it is proposed that a dual-process approach that takes into account both the reminding and recollection at test in the JOF task, as well as attempting to explain the influence of an underlying construct such as familiarity that effects both tasks may be the most appropriate explanation for frequency estimation results.

In recent years, the state-of-the-art in field programmable gate array (FPGA) technology has been advancing rapidly. Consequently, the use of FPGAs is being considered in many applications which have traditionally relied upon application-specific integrated circuits (ASICs). FPGA-based designs have a number of advantages over ASIC-based designs, including lower up-front engineering design costs, shorter time-to-market, and the ability to reconfigure devices in the field. However, ASICs have a major advantage in terms of computational resources. As a result, expensive high performance ASIC algorithms must be redesigned to fit the limited resources available in an FPGA. <p> Concurrently, coaxial cable television and internet networks have been undergoing significant upgrades that have largely been driven by a sharp increase in the use of interactive applications. This has intensified demand for the so-called upstream channels, which allow customers to transmit data into the network. The format and protocol of the upstream channels are defined by a set of standards, known as DOCSIS 3.0, which govern the flow of data through the network. <p> Critical to DOCSIS 3.0 compliance is the upstream demodulator, which is responsible for the physical layer reception from all customers. Although upstream demodulators have typically been implemented as ASICs, the design of an FPGA-based upstream demodulator is an intriguing possibility, as FPGA-based demodulators could potentially be upgraded in the field to support future DOCSIS standards. Furthermore, the lower non-recurring engineering costs associated with FPGA-based designs could provide an opportunity for smaller companies to compete in this market. <p> The upstream demodulator must contain complicated synchronization circuitry to detect, measure, and correct for channel distortions. Unfortunately, many of the synchronization algorithms described in the open literature are not suitable for either upstream cable channels or FPGA implementation. In this thesis, computationally inexpensive and robust synchronization algorithms are explored. In particular, algorithms for frequency recovery and equalization are developed. <p> The many data-aided feedforward frequency offset estimators analyzed in the literature have not considered intersymbol interference (ISI) caused by micro-reflections in the channel. It is shown in this thesis that many prominent frequency offset estimation algorithms become biased in the presence of ISI. A novel high-performance frequency offset estimator which is suitable for implementation in an FPGA is derived from first principles. Additionally, a rule is developed for predicting whether a frequency offset estimator will become biased in the presence of ISI. This rule is used to establish a channel excitation sequence which ensures the proposed frequency offset estimator is unbiased. <p> Adaptive equalizers that compensate for the ISI take a relatively long time to converge, necessitating a lengthy training sequence. The convergence time is reduced using a two step technique to seed the equalizer. First, the ISI equivalent model of the channel is estimated in response to a specific short excitation sequence. Then, the estimated channel response is inverted with a novel algorithm to initialize the equalizer. It is shown that the proposed technique, while inexpensive to implement in an FPGA, can decrease the length of the required equalizer training sequence by up to 70 symbols. <p> It is shown that a preamble segment consisting of repeated 11-symbol Barker sequences which is well-suited to timing recovery can also be used effectively for frequency recovery and channel estimation. By performing these three functions sequentially using a single set of preamble symbols, the overall length of the preamble may be further reduced.

In recent years, the state-of-the-art in field programmable gate array (FPGA) technology has been advancing rapidly. Consequently, the use of FPGAs is being considered in many applications which have traditionally relied upon application-specific integrated circuits (ASICs). FPGA-based designs have a number of advantages over ASIC-based designs, including lower up-front engineering design costs, shorter time-to-market, and the ability to reconfigure devices in the field. However, ASICs have a major advantage in terms of computational resources. As a result, expensive high performance ASIC algorithms must be redesigned to fit the limited resources available in an FPGA. <p> Concurrently, coaxial cable television and internet networks have been undergoing significant upgrades that have largely been driven by a sharp increase in the use of interactive applications. This has intensified demand for the so-called upstream channels, which allow customers to transmit data into the network. The format and protocol of the upstream channels are defined by a set of standards, known as DOCSIS 3.0, which govern the flow of data through the network. <p> Critical to DOCSIS 3.0 compliance is the upstream demodulator, which is responsible for the physical layer reception from all customers. Although upstream demodulators have typically been implemented as ASICs, the design of an FPGA-based upstream demodulator is an intriguing possibility, as FPGA-based demodulators could potentially be upgraded in the field to support future DOCSIS standards. Furthermore, the lower non-recurring engineering costs associated with FPGA-based designs could provide an opportunity for smaller companies to compete in this market. <p> The upstream demodulator must contain complicated synchronization circuitry to detect, measure, and correct for channel distortions. Unfortunately, many of the synchronization algorithms described in the open literature are not suitable for either upstream cable channels or FPGA implementation. In this thesis, computationally inexpensive and robust synchronization algorithms are explored. In particular, algorithms for frequency recovery and equalization are developed. <p> The many data-aided feedforward frequency offset estimators analyzed in the literature have not considered intersymbol interference (ISI) caused by micro-reflections in the channel. It is shown in this thesis that many prominent frequency offset estimation algorithms become biased in the presence of ISI. A novel high-performance frequency offset estimator which is suitable for implementation in an FPGA is derived from first principles. Additionally, a rule is developed for predicting whether a frequency offset estimator will become biased in the presence of ISI. This rule is used to establish a channel excitation sequence which ensures the proposed frequency offset estimator is unbiased. <p> Adaptive equalizers that compensate for the ISI take a relatively long time to converge, necessitating a lengthy training sequence. The convergence time is reduced using a two step technique to seed the equalizer. First, the ISI equivalent model of the channel is estimated in response to a specific short excitation sequence. Then, the estimated channel response is inverted with a novel algorithm to initialize the equalizer. It is shown that the proposed technique, while inexpensive to implement in an FPGA, can decrease the length of the required equalizer training sequence by up to 70 symbols. <p> It is shown that a preamble segment consisting of repeated 11-symbol Barker sequences which is well-suited to timing recovery can also be used effectively for frequency recovery and channel estimation. By performing these three functions sequentially using a single set of preamble symbols, the overall length of the preamble may be further reduced.

In applications, the true underlying model of an observed time series is typically unknown or has a complicated structure. A common approach is to approximate the true model by autoregressive (AR) equation whose orders are chosen by information criterions such as AIC, BIC and Parsen's CAT and whose parameters are estimated by the least square (LS), the Yule Walker (YW) or other methods. However, as sample size increases, it often implies that the model order has to be refined and the parameters need to be recalculated. In order to avoid such shortcomings, we propose the Regularized AR (RAR) approximation and illustrate its applications in frequency detection and long memory process forecasting. The idea of the RAR approximation is to utilize a “long" AR model whose order significantly exceeds the model order suggested by information criterions, and to estimate AR parameters by Regularized LS (RLS) method, which enables to estimate AR parameters with different level of accuracy and the number of estimated parameters can grow linearly with the sample size. Therefore, the repeated model selection and parameter estimation are avoided as the observed sample increases. We apply the RAR approach to estimate the unknown frequencies in periodic processes by approximating their generalized spectral densities, which significantly reduces the computational burden and improves accuracy of estimates. Our theoretical findings indicate that the RAR estimates of unknown frequency are strongly consistent and normally distributed. In practice, we may encounter spurious frequency estimates due to the high model order. Therefore, we further propose the robust trimming algorithm (RTA) of RAR frequency estimation. Our simulation studies indicate that the RTA can effectively eliminate the spurious roots and outliers, and therefore noticeably increase the accuracy. Another application we discuss in this thesis is modeling and forecasting of long memory processes using the RAR approximation. We demonstration that the RAR is useful in long-range prediction of general ARFIMA(p,d,q) processes with p > 1 and q > 1 via simulation studies.

In applications, the true underlying model of an observed time series is typically unknown or has a complicated structure. A common approach is to approximate the true model by autoregressive (AR) equation whose orders are chosen by information criterions such as AIC, BIC and Parsen's CAT and whose parameters are estimated by the least square (LS), the Yule Walker (YW) or other methods. However, as sample size increases, it often implies that the model order has to be refined and the parameters need to be recalculated. In order to avoid such shortcomings, we propose the Regularized AR (RAR) approximation and illustrate its applications in frequency detection and long memory process forecasting. The idea of the RAR approximation is to utilize a “long" AR model whose order significantly exceeds the model order suggested by information criterions, and to estimate AR parameters by Regularized LS (RLS) method, which enables to estimate AR parameters with different level of accuracy and the number of estimated parameters can grow linearly with the sample size. Therefore, the repeated model selection and parameter estimation are avoided as the observed sample increases. We apply the RAR approach to estimate the unknown frequencies in periodic processes by approximating their generalized spectral densities, which significantly reduces the computational burden and improves accuracy of estimates. Our theoretical findings indicate that the RAR estimates of unknown frequency are strongly consistent and normally distributed. In practice, we may encounter spurious frequency estimates due to the high model order. Therefore, we further propose the robust trimming algorithm (RTA) of RAR frequency estimation. Our simulation studies indicate that the RTA can effectively eliminate the spurious roots and outliers, and therefore noticeably increase the accuracy. Another application we discuss in this thesis is modeling and forecasting of long memory processes using the RAR approximation. We demonstration that the RAR is useful in long-range prediction of general ARFIMA(p,d,q) processes with p > 1 and q > 1 via simulation studies.

No description available.

Industrial processes have for a long time become more and more automated, this is no different in the mining industry. When excavating during mining operations special drill rigs are used to drill holes in the rock walls to be used for either explosives or bolts to support the structure. The study aimed to find out if it was possible to create an algorithm that would use the drill rigs telemetry data to estimate the number of holes it had created over specific time period. The main approach would be to see if machine learning could be used for the problem or if some other method could be theorised. Without the groundwork needed to create a proper machine learning algorithm a basic statistical approach was used to solve the problem, however since there were no actual reports containing the amount of holes a rig drilled the final solution is highly conjectural.

Three new and efficient carrier frequency offset estimators are created for the case of disjoint pilot symbol blocks. The estimators are efficient in both a statistical sense and a computational sense. They are formulated to reduce computational cost for use in real-time applications, such as FPGA (field programmable gate array) devices. A reduced cost maximum likelihood (ML) frequency estimator is described. It is a generalization of the approximate ML estimator for a single block of pilot symbols. A number of recent ML estimation techniques are integrated with the purpose of reducing the computational cost while preserving estimation performance. The estimator incorporates multirate signal processing methods, FFT periodogram searches, and directed periodogram searches. The subsequent relationships between FFT lengths, resampling rates, and search iterations is established. The proposed estimator exhibits very good accuracy, operating range, and a low SNR threshold, and has low cost. A data-aided frequency estimator based on the measurement of phase increments, is also derived. It has extremely low cost, but a high SNR threshold. However, its formulation is such that a careful analysis of the range error problem may be performed. From this analysis certain conclusions are made about proper pilot symbol organization, and these conclusions are applicable to other frequency estimators. The third estimator is a generalization of the autocorrelation frequency estimation technique. The generalizations are needed to account for the spacings between the pilot blocks. A novel iterative approach, incorporating a Kalman filter, is used to improve operating range. It is shown that the autocorrelation frequency estimator exhibits good accuracy while maintaining a useful operating range. Real-time architectures are described for the ML and autocorrelation frequency estimators using disjoint pilot blocks. The computational cost and estimation performance of the proposed estimators are analyzed and it is shown that they give estimation performance near to theoretical limits, while preserving wide operating range. We see that the autocorrelation estimator is appropriate for small numbers of pilot symbols, while the ML estimator is appropriate for large numbers of pilot symbols. The new frequency estimators are the first to be derived (for the case of disjoint blocks of pilot symbols) such that computational cost is kept low, while still achieving high accuracy, a wide operating range, and low SNR thresholds.

Spectral interferometry, also known as spectral-domain white light or low coherence interferometry, has seen numerous applications in sensing and metrology of physical parameters. It can provide phase or optical path information of interest in single shot measurements with exquisite sensitivity and large dynamic range. As fast spectrometer became more available in 21st century, spectral interferometric techniques start to dominate over time-domain interferometry, thanks to its speed and sensitivity advantage. In this work, a dual-modality phase/birefringence imaging system is proposed to offer a quantitative approach to characterize phase, polarization and spectroscopy properties on a variety of samples. An interferometric spectral multiplexing method is firstly introduced by generating polarization mixing with specially aligned polarizer and birefringence crystal. The retardation and orientation of sample birefringence can then be measured simultaneously from a single interference spectrum. Furthermore, with the addition of a Nomarski prism, the same setup can be used for quantitative differential interference contrast (DIC) imaging. The highly integrated system demonstrates its capability for noninvasive, label-free, highly sensitive birefringence, DIC and phase imaging on anisotropic materials and biological specimens, where multiple intrinsic contrasts are desired. Besides using different intrinsic contrast regime to quantitatively measure different biological samples, spectral multiplexing interferometry technique also finds an exquisite match in imaging single anisotropic nanoparticles, even its size is well below diffraction limit. Quantitative birefringence spectroscopy measurement over gold nanorod particles on glass substrate demonstrates that the proposed system can simultaneously determine the polarizability-induced birefringence orientation, as well as the scattering intensity and the phase differences between major/minor axes of single nanoparticles. With the anisotropic nanoparticles' spectroscopic polarizability defined prior to the measurement with calculation or simulation, the system can be further used to reveal size, aspect ratio and orientation information of the detected anisotropic nanoparticle. Alongside developing optical anisotropy imaging systems, the other part of this research describes our effort of investigating the sensitivity limit for general spectral interferometry based systems. A complete, realistic multi-parameter interference model is thus proposed, while corrupted by a combination of shot noise, dark noise and readout noise. With these multiple noise sources in the detected spectrum following different statistical behaviors, Cramer-Rao Bounds is derived for multiple unknown parameters, including optical pathlength, system-specific initial phase, spectrum intensity as well as fringe visibility. The significance of the work is to establish criteria to evaluate whether an interferometry-based optical measurement system has been optimized to its hardware best potential. An algorithm based on maximum likelihood estimation is also developed to achieve absolute optical pathlength demodulation with high sensitivity. In particular, it achieves Cramer-Rao bound and offers noise resistance that can potentially suppress the demodulation jump occurrence. By simulations and experimental validations, the proposed algorithm demonstrates its capability of achieving the Cramer-Rao bound over a large dynamic range of optical pathlengths, initial phases and signal-to-noise ratios. / PHD / Optical imaging is unique for its ability to use light to provide both structural and functional information from microscopic to macroscopic scales. As for microscopy, how to create contrast for better visualization of detected objects is one of the most important topic. In this work, we are aiming at developing a noninvasive, label-free and quantitative imaging technique based on multiple intrinsic contrast regimes, such as intensity, phase and birefringence. Spectral multiplexing interferometry method is firstly introduced by generating spectral interference with polarization mixing. Multiple parameters can thus be demodulated from single-shot interference spectrum. With Jones Matrix analysis, the retardation and orientation of sample birefringence can be measured simultaneously. A dual-modality phase/birefringence imaging system is proposed to offer a quantitative approach to characterize phase, polarization and spectroscopy properties on a variety of samples. The high integrated system can not only deliver label-free, highly sensitive birefringence, DIC and phase imaging of anisotropic materials and biological specimens, but also reveal size, aspect ratio and orientation information of anisotropic nanoparticles of which the size is well below diffraction limit. Alongside developing optical imaging systems based on spectral interferometry, the other part of this research describes our effort of investigating the sensitivity limit for general spectral interferometry based systems. The significance of the work is using Cramer-Rao Bounds to establish criteria to evaluate whether an optical measurement system has been optimized to its hardware best potential. An algorithm based on maximum likelihood estimation is also developed to achieve absolute optical pathlength demodulation with high sensitivity. In particular, it achieves Cramer-Rao bound and offers noise resistance that can potentially suppress the demodulation jump occurrence.

Instantaneous Frequency (IF) estimation based on time-varying autoregressive (TVAR) modeling has been shown to perform well in practical scenarios when the IF variation is rapid and/or non-linear and only short data records are available for modeling. A challenging aspect of implementing IF estimation based on TVAR modeling is the efficient computation of the time-varying coefficients by solving a set of linear equations referred to as the generalized covariance equations. Conventional approaches such as Gaussian elimination or direct matrix inversion are computationally inefficient for solving such a system of equations especially when the covariance matrix has a high order. We implement two recursive algorithms for efficiently inverting the covariance matrix. First, we implement the Akaike algorithm which exploits the block-Toeplitz structure of the covariance matrix for its recursive inversion. In the second approach, we implement the Wax-Kailath algorithm that achieves a factor of 2 reduction over the Akaike algorithm in the number of recursions involved and the computational effort required to form the inverse matrix. Although a TVAR model works well for IF estimation of frequency modulated (FM) components in white noise, when the model is applied to a signal containing a finitely correlated signal in addition to the white noise, estimation performance degrades; especially when the correlated signal is not weak relative to the FM components. We propose a decorrelating TVAR (DTVAR) model based IF estimation and a DTVAR model based linear prediction error filter for FM interference rejection in a finitely correlated environment. Simulations show notable performance gains for a DTVAR model over the TVAR model for moderate to high SIRs. / Master of Science