This work extends our recent work on proving that the particle lter converge for unbounded function to a more general case. More speci cally, we prove that the particle lter converge for unbounded functions in the sense of L-convergence, for an arbitrary p ≥ 2. Related to this, we also provide proofs for the case when the function we are estimating is bounded. In the process of deriving the mai...

Paraunitary lter banks are important for several signal processing tasks. In this paper, we consider the task of adapting the coeecients of a multichan-nel FIR paraunitary lter bank via gradient ascent or descent on a chosen cost function. The proposed generalized algorithms inherently adapt the system's parameters in the space of paraunitary l-ters. Modiications and simpliications of the techn...

Keywords| Filter banks, bi-orthogonal, linear phase, McClellan transformations, multirate systems. EDICS| Filter Bank Theory 2.4.2. Abstract| In this paper we provide a new method for analyzing multidimensional lter banks. This method enables us to solve various open problems in multidimensional l-ter bank characterization and design. The essential element in this new approach is the redeenitio...

FIR lter design problems in the frequency domain are nonlinear (semi-innnite) optimization problems. In practice these almost always have been solved in a simpliied form and/or only under restricting assumptions. In this paper, the four main design approximation problems in the frequency domain are stated in general forms, which allow the inclusion of constraints and the choice of an arbitrary ...

We examine the problem of approximating a complex frequency response by a real-valued FIR lter according to the L 2 norm subject to additional inequality constraints for the complex error function. Starting with the Kuhn-Tucker optimality conditions which specialize to a system of nonlinear equations we deduce an iterative algorithm. These equations are solved by Newton's method in every iterat...

The lter construction, as an endo-functor on the category of small coherent categories, was used extensively by A. Pitts in a series of papers in the 80's to prove completeness and interpolation results. Later I. Moerdijk and E. Palmgren used the lter construction to construct non-standard models of Heyting arithmetic. In this paper we describe lter construction as a left-adjoint: applied to a ...

In some situations where active noise control could be used, the well-known multichannel version of the ltered-X LMS adaptive lter is too computationally-complex to implement. In this paper, we develop a fast, exact implementation of this multichannel system whose complexity is approximately O(2L) per lter channel, where L is the FIR lter length. In addition, we provide a computationally-e cien...

We study the stability of the optimal lter w.r.t. its initial condition and w.r.t. the model for the hidden state and the observations in a general hidden Markov model, using the Hilbert projective metric. These stability results are then used to prove, under some mixing assumption, the uniform convergence to the optimal lter of several particle lters, such as the interacting particle lter and ...

Junction characterization is a very costly task since junctions are multi-scalar and multi-oriented structures. Besides, high directional selectivity is also required to deal with complex junctions. Steerable lters attenuate this computational burden by approximating a lter at an arbitrary scale and orientation with a-nite set of so-called basis lters. But due to the uncertainty principle high ...

In this paper, we e v aluate the performance limitations of subband adaptive lters in terms of achievable nal error terms. The limiting factors are the aliasing level in the subbands, which poses a distortion and thus presents a l o wer bound for the minimum mean squared error in each subband, and the distortion function of the overall lter bank, which in a system identiication setup restricts ...