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The problem of estimating the frequencies of sinusoidal components from a finite number of noisy discrete-time measurements has attracted a great deal of attention and still is an active research area to date, because of its wide applications in science and engineering. In this presentation, simple and accurate solutions for sinusoidal frequency estimation of 1D and 2D signals in the presence of additive white Gaussian noise are presented.


Finding the position of a target based on measurements from an array of spatially separated sensors has been an important problem in radar, sonar, global positioning system, mobile communications, multimedia and wireless sensor networks. Time-of-arrival (TOA), time-difference-of-arrival (TDOA), received signal strength (RSS) and direction-of-arrival (DOA) of the emitted signal are commonly used measurements for source localization. Basically, TOAs, TDOAs and RSSs provide the distance information between the source and sensors while DOAs are the source bearings relative to the receivers.


Analyzing the performance of estimators is a typical task in signal processing. Two fundamental performance measures in the aspect of accuracy are bias and mean square error (MSE). In this presentation, we revisit a simple technique to produce the bias and MSE of an estimator that minimizes or maximizes an unconstrained differentiable cost function over a continuous space of the parameter vector under the small error conditions. This presentation is a companion work of: H. C. So, Y. T. Chan, K. C. Ho and Y.


This theoretical paper aims to provide a probabilistic framework for graph signal processing. By modeling signals on graphs as Gaussian Markov Random Fields, we present numerous important aspects of graph signal processing, including graph construction, graph transform, graph downsampling, graph prediction, and graph-based regularization, from a probabilistic point of view.