This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under typical frequency transformations, such as lowpass-lowpass, lowpasshighpass, lowpass-bandpass, and lowpass-bandstop transformations. Our main result establishes the fact that the second-order modes are invariant under any of these typical frequency transformations. This m...

Filters of some sort are essential to the operation of most electronic circuits. It is therefore in the interest of anyone involved in electronic circuit design to have the ability to develop filter circuits capable of meeting a given set of specifications. delay time steady state error, operating frequency, and wavelength, damping frequency, and wavelength the major interesting design paramete...

—The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain theoretical insights into the performance of this algorithm, we examine its mean-square convergence and derive an expression for its steady-state mean-square deviation. Ou...

This paper presents a new algorithm that can solve the problem of selecting appropriate update step size in the LMS algorithm. The proposed algorithm, called a Complementary Pair LMS (CP-LMS) algorithm, consists of two adaptive lters with di erent update step sizes operating in parallel, one lter re-initializing the other with the better coe cient estimates whenever possible. This new algorithm...

In this paper, we propose a novel method to compensate the effect of the noise for Automatic Speech Recognition in car environments. This method can be applied to recognizers using a standard MFCC front-end. We perform a channel-by-channel compensation of the noise effect in the filter-bank output domain. In a first stage, the parameters describing the noise are estimated and secondly, we estim...

We consider the fuzzification of the notion of a positive implicative ordered filter in implicative semigroups. We show that every fuzzy positive implicative ordered filter is both a fuzzy ordered filter and a fuzzy implicative ordered filter. We give examples that a fuzzy (implicative) ordered filter may not be a fuzzy positive implicative ordered filter. We also state equivalent conditions of...

The unscented Kalman filter (UKF) is formulated for the continuous-discrete state space model. The exact moment equations are solved approximately by using the unscented transform (UT) and the measurement update is obtained by computing the normal correlation, again using the UT. In contrast to the usual treatment, the system and measurement noise sequences are included from the start and are n...

Despite all the progress in filtering algorithms for state estimation in very high dimensional systems, the technology is delicate and sometimes difficult to apply. Good initialization of filter gain, appropriate choice of tuning parameters and their optimization are the key factors to achieve robust high-performance filtering algorithms. In this paper the authors propose a method for properly ...

In this paper we study ergodic properties of hidden Markov models with a generalized observation structure. In particular sufficient conditions for the existence of a unique invariant measure for the pair filter-observation are given. Furthermore, necessary and sufficient conditions for the existence of a unique invariant measure of the triple state-observation-filter are provided in terms of a...

In this paper, we investigate a long state vector Kalman filter for the enhancement of speech that has been corrupted by white and coloured noise. It has been reported in previous studies that a vector Kalman filter achieves better enhancement than the scalar Kalman filter and it is expected that by increasing the state vector length, one may improve the enhancement performance even further. Ho...