ELEC3540 Lecture 9 Matched Filter

IEEE Transactions on Information Theory, 1960

ANNUAL JOURNAL OF TECHNICAL UNIVERSITY OF VARNA, BULGARIA, 2017

A one model of parametrically controlled coherent filters is described and analyzed, applied also in radar systems and mobile communication systems to improve noise resistance. Application of the Nyquist-Shannon theorem in the frequency domain to obtain a set of frequency filters with variable parameters. The conversion of the signal at the output of the parameter filter using the auto correlation feature is shown when a normal white noise occurs.

IEEE Transactions on Signal Processing, 2012

The conjugate gradient (CG) algorithm is an efficient method for the calculation of the weight vector of the matched filter (MF). As an iterative algorithm, it produces a series of approximations to the MF weight vector, each of which can be used to filter the test signal and form a test statistic. This effectively leads to a family of detectors, referred to as the CG-MF detectors, which are indexed by the number of iterations incurred. We first consider a general case involving an arbitrary covariance matrix of the disturbance (including interference, noise, etc.) and show that all CG-MF detectors attain constant false alarm rate (CFAR) and, furthermore, are optimum in the sense that the th CG-MF detector yields the highest output signal-to-interference-and-noise ratio (SINR) among all linear detectors within the th Krylov subspace. We then consider a structured case frequently encountered in practice, where the covariance matrix of the disturbance contains a low-rank component (rank-) due to dominant interference sources, a scaled identity due to the presence of a white noise, and a perturbation component containing the residual interference. We show that the (+1)st CG-MF detector achieves CFAR and an output SINR nearly identical to that of the MF detector which requires complete iterations of the CG algorithm till reaching convergence. Hence, the (+1)st CG-MF detector can be used in place of the MF detector for significant computational saving when is small. Numerical results are presented to verify the accuracy of our analysis for the CG-MF detectors.

SPIE Proceedings, 1980

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IEEE Transactions on Signal Processing, 1991

A matched filter's performance is strongly related to the signal being detected, and can be shown to be optimal when that signal is an eigenvector of the noise correlation matrix corresponding to a minimum eigenvalue. When fewer correlations are known than would be necessary to specify such an eigenvector, it is natural to choose a signal which is robust to the implied uncertainty in the noise dependency structure. This is shown to be tantamount to finding a tight upper bound on the minimum eigenvalue over all correlation matrices within the uncertainty class. Such a bound is achieved by the reduced correlation matrix of order equal to the number of available correlations, and hence the robust signal is shown to have this length. No matter how reasonable, any assumption used to extend the correlation matrix can degrade performance; a system designer should not try to use information he or she does not have. -Original ----Linear Quadrafic QL -I. INTRODUCTION Pm 1.0 Fig. 4. Noise-in-noise with unequal means-GD. Signal + noise mean = 150, signal + noise variance = 1800, noise mean = 100, noise variance = 900.

Cornell University - arXiv, 2011

A fundamental problem in wireless communication is the time-frequency shift (TFS) problem: Find the timefrequency shift of a signal in a noisy environment. The shift is the result of time asynchronization of a sender with a receiver, and of non-zero speed of a sender with respect to a receiver. A classical solution of a discrete analog of the TFS problem is called the matched filter algorithm. It uses a pseudo-random waveform S(t) of the length p, and its arithemtic complexity is O(p 2 • log(p)), using fast Fourier transform. In these notes we introduce a novel approach of designing new waveforms that allow faster matched filter algorithm. We use techniques from group representation theory to design waveforms S(t), which enable us to introduce two fast matched filter (FMF) algorithms, called the flag algorithm, and the cross algorithm. These methods solve the TFS problem in O(p • log(p)) operations. We discuss applications of the algorithms to mobile communication, GPS, and radar.

The aim of this paper is to present the details of signal processing techniques in Military RADARS . These techniques are strongly based on mathematics and specially on stochastic processes. Detecting a target in a noisy environment is a many folds sequential process. The signal processing chain only provides to the overall system boolean indicators stating the presence (or not) of targets inside the coverage area. It is part of the strategical operation of the radar. This paper mainly focuses on Design of Matched filter and generation of chirp Signal.

2011

In common text on communications and signal processing matched filters are derived from maximum output SNR of a linear time invariant system on a determined point. The question “is match filter best system (Linear or not) to detect a specific signal?” is not usually considered. Here we consider this question with restriction to Gaussian noise and framework of sufficient estimator.

Stochastic Control, 2010

Stochastic Control 272 2. Random signal expansion 2.1 1-D discrete-time signals Let S be a zero mean, stationary, discrete-time random signal, made of M successive samples and let {s 1 , s 2 ,. .. , s M } be a zero mean, uncorrelated random variable sequence, i.

2017

In this work we study a particular filter synthesis problem in order to minimize the reflection coefficient of the global system consisting of filter and antenna. The matching problem is formulated as an optimization problem involving the minimization of a pseudo hyperbolic distance and the solution to this problem using H ∞ approach yields a lower bound for the matching criterion related to the computation of a matching filter, with prescribed finite degree, under selectivity constraints.