Choice of Sampling Interval and Extent for Finite-Energy Fields

We focus on the problem of representing a nonstationary finite-energy random field, with finitely many samples. We do not require the field to be of finite extent or to be bandlimited. We propose an optimizable procedure for obtaining a finite-sample representation of the given field. We estimate the reconstruction error of the procedure, showing that it is the sum of the truncation errors in the space and frequency domains. We also optimize the truncation parameters analytically and present the resultant Pareto-optimal tradeoff curves involving the error in reconstruction and the sample count, for several examples. These tradeoff curves can be used to determine the optimal sampling strategy in a practical situation based on the relative importance of error and sample count for that application. © 2016 IEEE

Computation of the one-dimensional unwrapped phase

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 101-102). "Cepstrum bibliography" (p. 67-100).In this thesis, the computation of the unwrapped phase of the discrete-time Fourier transform (DTFT) of a one-dimensional finite-length signal is explored. The phase of the DTFT is not unique, and may contain integer multiple of 27r discontinuities. The unwrapped phase is the instance of the phase function chosen to ensure continuity. This thesis presents existing algorithms for computing the unwrapped phase, discussing their weaknesses and strengths. Then two composite algorithms are proposed that use the existing ones, combining their strengths while avoiding their weaknesses. The core of the proposed methods is based on recent advances in polynomial factoring. The proposed methods are implemented and compared to the existing ones.by Zahi Nadim Karam.S.M

Generalized DFT: extensions in communications

Discrete Fourier Transform (DFT) is a restricted version of Generalized DFT (GDFT) which offers a very limited number of sets to be used in a multicarrier communication system. In contrast, as an extension on Discrete Fourier Transform (DFT) from the linear phase to non-linear phase, the proposed GDFT provides many possible carrier sets of various lengths with comparable or better performance than DFT. The availability of the rich library of orthogonal constant amplitude transforms with good performance allows people to design adaptive systems where user code allocations are made dynamically to exploit the current channel conditions in order to deliver better performance. For MIMO Radar systems, the ideal case to detect a moving target is when all waveforms are orthogonal, which can provide an accurate estimation. But this is not practical in distributed MIMO radars, where sensors are at varying distances from a target. Orthogonal waveforms with low auto- and cross-correlations are of great interest for MIMO radar applications with distributed antennas. Finite length orthogonal codes are required in real-world applications where frequency selectivity and signal correlation features of the optimal subspace are compromised. In the first part of the dissertation, a method is addressed to design optimal waveforms which meets above requirements for various radar systems by designing the phase shaping function (PSF) of GDFT framework with non-linear phase. Multicarrier transmission such as orthogonal frequency-division multiplexing (OFDM) has seen a rise in popularity in wireless communication, as it offers a promising choice for high speed data rate transmission. Meanwhile, high peak-to-average power ratio (PAPR) is one of the well-known drawbacks of the OFDM system due to reduced power efficiency in non-linear modules. Such a situation leads to inefficient amplification and increases the cost of the system, or increases in interference and signal distortion. Therefore, PAPR reduction techniques play an essential role to improve power efficiency in the OFDM systems. There has been a variety of PAPR reduction methods emphasizing different aspects proposed in the literature. The trade-off for PAPR reduction in the existing methods is either increased average power and/or added computational complexity. A new PAPR reduction scheme is proposed that implements a pre-designed symbol alphabet modifier matrix (SAM) to jointly modify the amplitude and phase values of the original data symbol alphabets prior to the IFFT operation of an OFDM system at the transmitter. The method formulated with the GDFT offers a low-complexity framework in four proposed cases devised to be independent of original data symbols. Without degrading the bit error rate (BER) performance, it formulates PAPR reduction problem elegantly and outperforms partial transmit sequences (PTS), selected mapping technique (SLM) and Walsh Hadamard transform (WHT-OFDM) significantly for the communication scenarios considered in the dissertation

Computer program for fast Karhunen Loeve transform algorithm

The fast KL transform algorithm was applied for data compression of a set of four ERTS multispectral images and its performance was compared with other techniques previously studied on the same image data. The performance criteria used here are mean square error and signal to noise ratio. The results obtained show a superior performance of the fast KL transform coding algorithm on the data set used with respect to the above stated perfomance criteria. A summary of the results is given in Chapter I and details of comparisons and discussion on conclusions are given in Chapter IV

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

A real-time data mining technique applied for critical ECG rhythm on handheld device

Sudden cardiac arrest is often caused by ventricular arrhythmias and these episodes can lead to death for patients with chronic heart disease. Hence, detection of such arrhythmia is crucial in mobile ECG monitoring. In this research, a systematic study is carried out to investigate the possible limitations that are preventing the realisation of a real-time ECG arrhythmia data-mining algorithm suitable for application on mobile devices. Based on the findings, a computationally lightweight algorithm is devised and tested. Ventricular tachycardia (VT) is the most common type of ventricular arrhythmias and is also the deadliest.. A ventricular tachycardia (VT) episode is due to a disorder ofthe regular contractions ofthe heart. It occurs when the human heart ventricles generate a rapid heartbeat which disrupts the regular physiology cycle. The normal sinus rhythm (NSR) of a regular human heart beat signal has its signature PQRST waveform and in regular pattern. Whereas, the characteristics of a ventricular tachycardia (VT) signal waveforms are short R-R intervals, widen QRS duration and the absence of P-waves. Each type of ECG arrhythmia previously mentioned has a unique waveform signature that can be exploited as features to be used for the realization of an automated ECG analysis application. In order to extract this known ECG waveform feature, a time-domain analysis is proposed for feature extraction. Cross-correlation allows the computation of a co-efficient that quantifies the similarity between two times-series. Hence, by cross-correlating known ECG waveform templates with an unknown ECG signal, the coefficient can indicate the similarities. In previous published work, a preliminary study was carried out. The cross-correlation coefficient wave (CCW) technique was introduced for feature extraction. The outcome ofthis work presents CCW as a promising feature to differentiate between NSR, VT and Vfib signals. Moreover, cross-correlation computation does not require high computational overhead. Next, an automated detection algorithm requires a classification mechanism to make sense of the feature extracted. A further study is conducted and published, a fuzzy set k-NN classifier was introduced for the classification of CCW feature extracted from ECG signal segments. A training set of size 180 is used. The outcome of the study indicates that the computationally light-weight fuzzy k-NN classifier can reliably classify between NSR and VT signals, the class detection rate is low for classifying Vfib signal using the fuzzy k-NN classifier. Hence, a modified algorithm known as fuzzy hybrid classifier is proposed. By implementing an expert knowledge based fuzzy inference system for classification of ECG signal; the Vfib signal detection rate was improved. The comparison outcome was that the hybrid fuzzy classifier is able to achieve 91.1% correct rate, 100% sensitivity and 100% specificity. The previously mentioned result outperforms the compared classifiers. The proposed detection and classification algorithm is able to achieve high accuracy in analysing ECG signal feature of NSR, VT and Vfib nature. Moreover, the proposed classifier is successfully implemented on a smart mobile device and it is able to perform data-mining of the ECG signal with satisfiable results

TV Black-space Spectrum Access for Wireless Local Area and Cellular Networks

This thesis presents a black-space spectrum access scheme for overlay cognitive radio in TV band. Physical layer implementations of secondary systems using software defined radio technology have been proposed. We consider two types of secondary transmitters with WLAN-type and LTE-type frame structures in order to study the impact of secondary transmission over primary pilot carriers on performances of channel estimation and interference cancellation algorithms. Bit error rate has been used as performance metric, and performances of the two secondary systems have been presented in different scenarios. The effect of secondary transmitters interference power level on performances of primary and secondary receivers has been investigated

Analysis and correction of the helium speech effect by autoregressive signal processing

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