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Fundamentals Of Adaptive Filtering Sayed Pdf 14 \/\/TOP\\\\

This paper proposes a new computation procedure of the Laplace-Gaussian filtering in the framework of adaptive filtering.The adaptive Laplace filtering is based on a fast implementation of the straightforward Laplace impulse response (IR). Also, a polynomial expansion is used to obtain the IR for each sample, which leads to a low computational complexity. This makes it possible to perform a high-speed computational processing. A numerical analysis is performed to confirm the performance of the Laplace-Gaussian IR.

fundamentals of adaptive filtering sayed pdf 14

We define a new class of importance sampling algorithms (ISAs) which are based on the Minimum Description Length (MDL) principle. These algorithms belong to the novel branch of adaptive sampling (AS). AS serves as an umbrella term for the various adaptive sampling algorithms that have emerged over the last two decades. The main goal of AS is to improve Monte Carlo estimators by actively updating the importance sampling distributions at each iteration using the information from the past. In this paper, we use an ensemble of ISAs to estimate the marginal log-likelihood of a specific N-dimensional real-valued function from a finite sample of $N$ independent and identically distributed (i.i.d.) realizations. We analyze the statistical behavior of the ISAs when applied to the estimation of Gaussian and Laplace probability distributions. Our simulations show that the ISAs converge faster to a target probability distribution, and their performance is better than the Pareto ISA when the tail of the target probability distribution is steep.

In this paper, we propose a novel class of adaptive estimators which iteratively construct a sequence of filters. Each filter is based on a static kernel and an automatic tuning parameter. The static kernel produces a Gaussian kernel when the tuning parameter takes the value of 1. The performance of the filters based on the Gaussian kernel improves when the tuning parameter increases. We theoretically and empirically evaluate the performance of the filters. We have presented results on simulated and real-world data to show the stability and effectiveness of the proposed adaptive filters. The ability of the proposed filters to effectively estimate the parameters of the kernel is validated in the estimation of parameters of the kernel.

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