By Stergios Stergiopoulos
Advances in electronic sign processing algorithms and machine expertise have mixed to supply real-time structures with features a ways past these of simply few years in the past. Nonlinear, adaptive tools for sign processing have emerged to supply higher array achieve functionality, notwithstanding, they lack the robustness of traditional algorithms. The problem is still to improve an idea that exploits some great benefits of both-a scheme that integrates those tools in useful, real-time systems.The complex sign Processing guide is helping you meet that problem. past delivering a superb advent to the foundations and purposes of complex sign processing, it develops a primary processing constitution that takes benefit of the similarities that exist between radar, sonar, and scientific imaging platforms and integrates traditional and nonlinear processing schemes.
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Extra info for Advanced Signal Processing Handbook
This constraint limits the ability of a linear adaptive filter to extract information from input data that are non-Gaussian. Despite its theoretical importance, the existence of Gaussian noise is open to question (Johnson and Rao, 1990). Moreover, non-Gaussian processes are quite common in many signal processing applications encountered in practice. The use of a Wiener filter or a linear adaptive filter to extract signals of interest in the presence of such non-Gaussian processes will therefore yield suboptimal solutions.
The resulting linear adaptive filters are referred to as square-root adaptive filters, because in a matrix sense they represent the square-root forms of the standard RLS algorithm. , a priori error signal) at time n l = exponential weighting factor k(n) = gain vector at time n P(n) = weight-error correlation matrix Initialize the algorithm by setting P(0) = δ∠1I, δ = small positive constant w(0) = 0 For each instant of time, n - 1, 2, …, compute λ P ( n – 1 )u ( n ) k ( n ) = ---------------------------------------------------------------–1 H 1 + λ u ( n )P ( n – 1 )u ( n ) –1 ˆ ( n – 1 )u ( n ) ξ(n) = d(n) – w H ˆ (n) = w ˆ ( n – 1 ) + k ( n )ξ ( n ) w * λ P ( n – 1 ) – λ k ( n )u ( n )P ( n – 1 ) –1 –1 3.
4 and given the set of reflection coefficients κ1, κ2, …, κM – 1, we may determine the final pair of outputs fM – 1(n) and bM – 1(n) by moving through the lattice predictor, stage by stage. For a correlated input sequence u(n), u(n – 1), …, u(n – M + 1) drawn from a stationary process, the backward prediction errors b0, b1(n), …, bM – 1(n) form a sequence of uncorrelated random variables. Moreover, there is a one-to-one correspondence between these two sequences of random variables in the sense that if we are given one of them, we may uniquely determine the other and vice versa.