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Discriminative, Generative and Imitative Learning - Jebara (2002) (Correct)
....It is interesting to note that in the case of no missing data, the above objective function simplifies back to the regular fully labeled SVM case. The above objective function can be maximized via axisparallel techniques. It is also important to use various matrix identities (i.e. some by Kailath [108] and some matrix partitioning techniques [121] to make the optimization efficient. This optimization gives us the desired values to specify the distribution P ( Theta; fl; y) This constrained optimization problem can be solved in an axis parallel manner (similar to Platt s SMO algorithm) In ....
T. Kailath. Linear Systems. Prentice-Hall, Englewood Cliffs, NJ, 1980.
On the Identification of Certain Noisy FIR Convolutive.. - Hachem, Desbouvries.. (Correct)
....UXWXWXWXU characterized by the fact : the rational matrix valued function is said to have a normal rank equal to . admits polynomial bases. A polynomial basis UXWXWOWXU is said to be minimal if is minimum (see [10] for more details) All minimal bases share the same degrees are characterized by the well known criterion (see [8] 10] Proposition 1 The polynomial basis UXWXWXWOU is minimal if and only if the matrix polynomial : U OU is ....
....to have a normal rank equal to . admits polynomial bases. A polynomial basis UXWXWOWXU is said to be minimal if is minimum (see [10] for more details) All minimal bases share the same degrees are characterized by the well known criterion (see [8] [10]) Proposition 1 The polynomial basis UXWXWXWOU is minimal if and only if the matrix polynomial : U OU is irreducible and column reduced. Usually, the minimal degrees are called the Kronecker indices associated to . The ....
T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, 1980
Stochastic Observability And Fault Diagnosis Of Additive.. - Gustafsson (Correct)
....B CA . C C C C The straightforward generalization of observability to timevarying systems follows from (5) as the condition of full rank of B B B B . C C C C from which the square observability Gramian is defined in the control literature (see for example [5]) t . 15) For stochastic systems, the definition is ( t . 16) However, in practice these measures are a bit dull, since they do not say anything about the FNR; they just answer yes or no. To answer the question which (fault) states are observable and distinguishable from ....
T. Kailath, Linear systems, Prentice-Hall, Englewood Cliffs, NJ, 1980.
Best Choice of Coordinate System for Tracking Coordinated Turns - Gustafsson, Isaksson (1996) (1 citation) (Correct)
....Q will be used in the simulations. It has turned out from simulations that the result is rather insensitive to how Q is computed. Neglecting the second order term in (3) and the noise, the solution of (6) can be written explicitely. From standard theory on sampled systems, see for instance [7], the continuous time system x(t) Ax(t) Bu(t) has a discrete time counterpart x(t T ) e AT x(t) Bd u(t) This assumes that the input u(t) is constant during the sampling interval. The discretized system can be written (notice that what corresponds to the input, f(x) Gamma ....
T. Kailath. Linear systems. Prentice-Hall, Englewood Cliffs, N.J., 1980.
Algorithms for Coupled Transient Simulation of Circuits.. - Silveira, Kamon, White (1994) (1 citation) (Correct)
....Az Bu, z]n, u]m y = C, Y ]P (15) whose transfer function is G(s) C(sI A) IB. Since we assume that (15) corresponds to passive in terconnect, the transfer function is stable, i.e. all the poles (or equivalently all the eigenvalues of the matrix A) are in the left half plane. It is well known [9] that for a given transfer function, the choice of the triplet [A, B, C] is not unique. Indeed, a linear coordi nate transformation T in the state space modifies the triplet [A, B, C] to [A, B, C] without modifying the transfer function. For the specific purpose of extract ing stable ....
Thomas Kailath. Linear Systems. Information and System Science Series. Prentice-Hall, Engle- wood Cliffs, New Jersey, First edition, 1980.
Stabilization of Large Linear Systems - He, Mehrmann (1994) (4 citations) Self-citation (Theory) (Correct)
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T. Kailath, Systems Theory, Prentice-Hall, Englewood Cliffs, New York, 1980.
Structured and Reduced Dimension Explicit Linear Quadratic - Regulators For Systems (2002) Self-citation (Systems) (Correct)
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T. Kailath, Linear Systems, Prentice Hall, Englewood Cliffs, N.J., 1980.
Adaptive Wiener Filters for Time-Varying Channel.. - Schafhuber, Matz.. (2003) (2 citations) Self-citation (Systems) (Correct)
.... Fourier transform of a strictly anticausal sequence (because (4) is 0 for n 0) We now use the spectral factorization = # l F l (#)F # l (#) 8) where F l (#) # n=0 f l [n] e with f l [n] minimum phase and monic ( f l [0] 1) From the monicity property, it follows that [12] # l = exp ln . The factorization (8) is guaranteed to exist because # l # due to # # 0, i.e. the Paley Wiener condition is satisfied [12] Inserting (8) into (7) and identifying the causal parts of both sides of the resulting equation yields the optimal filter ....
....= # n=0 f l [n] e with f l [n] minimum phase and monic ( f l [0] 1) From the monicity property, it follows that [12] # l = exp ln . The factorization (8) is guaranteed to exist because # l # due to # # 0, i.e. the Paley Wiener condition is satisfied [12]. Inserting (8) into (7) and identifying the causal parts of both sides of the resulting equation yields the optimal filter transfer functions C l,opt (#) 1 P# l F l (#) l = 0,1, L 1 . 9) A Doppler domain expression of the MMSE is obtained from (6) N# l=0 # C ....
T. Kailath, Linear Systems. Englewood Cliffs (NJ): Prentice Hall, 1980.
Subspace Based Signal Analysis using Singular Value.. - van der Veen.. (1993) (5 citations) Self-citation (Systems) (Correct)
....some system theoretic notions with relevance to subspace based system realization theory. Section 3. will apply this theory to a few standard identification scenarios that will be used throughout this paper. More background material on linear systems theory can be found in the books by Kailath [12] and Rugh [13] 2.1. System operator Consider a causal linear time invariant (LTI) system with system transfer op erator T, mapping an input vector (sequence) that represents an input signal U [ 1 1 . T to a corresponding output sequence Y [ Y [ Y . T, such that y Tu ....
....state similarity transformation that will diagonaJize the A matrix: A RR . This is an eigenvaJue decomposition of A, and the entries of are the eigenvaJues of A. A sufficient condition for the existence of this decomposition (ie, an invertible R) is that the poles of the system be distinct [12] 2.3. Hankel operator We now turn to the reaJization problem: given a system transfer operator T (or equivaJently an impulse response h) how can a state space model that reaJizes this transfer operator be determined The solution to the reaJization problem in a subspace context calls for the ....
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T. Kailath, Linear Systems. Prentice Hall, Englewood Cliffs, N J, 1980.
Recent developments in blind channel equalization: From.. - Liu, Xu, Tong, Kailath (1996) (23 citations) Self-citation (Kailath Systems) (Correct)
....blocks (17) c3 h3(0) y(k) s(k) u(k) 19) cM h(0) c, h: i) hi(O)h(1) h, L) h, O)h(L) The transfer matrix of the above model is [h2(z) hu(z) T C(zI ) a= h: z) 20) 90 H. Liu et al. Signal Processing 50 (1996) 83 99 Using standard system identification results [23,31], it is now clear that Theorem 2 can be restated in the following more informative format [51,33, 11,26] if y, ohi(k)z k are coprime, i.e. they do not share any common roots. Note that in the above theorems, no requirement regarding the inputs is specified. For most statistics based ....
....they do not share any common rOOtS s(1) s(N) contain no fewer than 2L 1 modes The number of modes, often referred to as the linear complexity, is a measurement of the diversity in a finite sequence. It can be analogous to the number of frequency components in an infinite data sequence [23,31]. Interestingly, the above conditions are the same as those for identifying a rational function with denominator and numer ator both of order L [31] It is true that the system under consideration is only FIR, and can be sufficiently identified with a known input s( that has L I modes ....
T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, 1980.
Blind Channel Identification Based on Second-Order Statistics: A.. - Member (1995) (30 citations) Self-citation (Kailath) (Correct)
....(24) c(z) F ( z ) 25) Proof. We first note that, in applying Leinma 2 to ( D ( z ) c(z) we deal with a (T 1) x 1 polynomial vector Next, we argue that there are exactly L cmnmon zeros among F( z) if and only if the minimal state space realization of D(z) c(z) has order L (see [7]) i.e, Y] L. By applying Lemma 2 with r = 1, we conclude that the channel is identifiable if and only if rank( D,c) l T l)k ] k v) 26) which leads directly to (23) Remark. An interesting iinplication of this theorem and Lemma 2 is that, for T = 2, the channel order can be determined by ....
T. Kailath, Linear Systems. Englewood Cliffs, NJ; Prentice-Hall, 1980.
Theory Of Mimo Biorthogonal Partners And Their Application .. - Vrcelj, Vaidyanathan (2001) Self-citation (Systems) (Correct)
....or even unstable depending on the matrix G(z) One important issue therefore is how to find an FIR biorthogonal partner and under what conditions it is possible to find one. In the next theorem we address this issue. In the following, the symbol grcd[ represents the greatest right common divisor [3], 2] Theorem 2. Existence of FIR LBP. Suppose F(z) is causal and FIR, given by the Type 2 polyphase form as in (1) Then there exists a causal FIR matrix H(z) such that [H(z)F(z) #M = I if and only if grcd[F0(z) F1(z) FM 1 (z) is a unimodular matrix R(z) Example 2. Given an ....
....2. First we consider the case M = 2. If F0(z) and F1(z) are right coprime (which is equivalent to saying that R(z) i.e. the grcd[F0 (z) F1(z) is unimodular) then there exist polynomial matrices H0(z) and H1 (z) such that H0(z)F0(z) H1(z)F1(z) I. This follows from the simple Bezout identity [3]. In fact, from the construction for a grcd (also in [3] it follows that there exists a unimodular matrix U(z) such that z U(z) R(z) 8) where all the building blocks above are L L matrices and U(z) is a 2L 2L matrix. Now we see that in this case we can choose H0 (z) ....
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T. Kailath, Linear Systems, Prentice Hall, Inc., Englewood Cliffs, N.J., 1980.
Unknown - (Correct)
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T. Kailath. Linear Systems. Prentice Hall, Englewood Cliffs, New Jersey, 1980.
Level Crossing Sampling in Feedback Stabilization under - Data-Rate Constraints Ernesto (Correct)
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T. Kailath, Linear Systems, Prentice Hall, Englewood Cliffs, NJ, 1980.
Behavioral Level Guidance Using Property-Based Design.. - Lisa Marie Guerra (1996) (1 citation) (Correct)
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T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, 1980.
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T. Kailath. Linear Systems. Prentice Hall, Englewood Cliffs, N.J., 1980.
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T. Kailath. Linear Systems. Prentice Hall,Englewood Cliffs, NJ., 1980.
On Computing Inner-Outer Factorizations of Rational Matrices - Varga (1995) (2 citations) (Correct)
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T. Kailath. Linear Systems. Prentice Hall, Englewood Cliffs, N.J., 1980.
Mimo Fir Equalizers And Orders - Ravikiran Rajagopal And (Correct)
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T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, N.J., 1980.
Multicarrier Equalization: Unification and.. - Martin, Vanbleu.. (2003) (Correct)
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T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, 1980.
Dynamic Texture Segmentation - Doretto, Cremers, Favaro, Soatto (2003) (1 citation) (Correct)
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T. Kailath. Linear Systems. Prentice Hall,Englewood Cliffs, NJ., 1980.
Time-Frequency Projection Filters: Online Implementation, - Subspace Tracking And (Correct)
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T. Kailath, Linear Systems. Englewood Cliffs (NJ): Prentice Hall, 1980.
New Results On Pole-Shifting For - Parametrized Families Of (Correct)
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Kailath,T., Linear Systems, Prentice Hall, Englewood Cliffs, 1980.
Some New Matrix Formulas Related To Hermite Matrix Polynomials.. - Jodar, Defez (1996) (Correct)
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T. Kailath: Linear Systems. (Prentice-Hall, Inc, Englewood Cliffs, New York, 1980).
A Study of Optimality in the H∞ Loop-Shaping Design Method - Feng (1995) (Correct)
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T. Kailath. Linear Systems. Prentice-Hall, Englewood Cliffs, N.J., 1980.
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