A state space approach to the design of globally optimal FIR energycompaction filters

We introduce a new approach for the least squared optimization of a weighted FIR filter of arbitrary order N under the constraint that its magnitude squared response be Nyquist(M). Although the new formulation is general enough to cover a wide variety of applications, the focus of the paper is on optimal energy compaction filters. The optimization of such filters has received considerable attention in the past due to the fact that they are the main building blocks in the design of principal component filter banks (PCFBs). The newly proposed method finds the optimum product filter F_opt(z)=H_opt(Z)H_opt (z^-1) corresponding to the compaction filter H_opt (z). By expressing F(z) in the form D(z)+D(z^-1), we show that the compaction problem can be completely parameterized in terms of the state-space realization of the causal function D(z). For a given input power spectrum, the resulting filter F_opt(z) is guaranteed to be a global optimum solution due to the convexity of the new formulation. The new algorithm is universal in the sense that it works for any M, arbitrary filter length N, and any given input power spectrum. Furthermore, additional linear constraints such as wavelets regularity constraints can be incorporated into the design problem. Finally, obtaining H_opt(z) from F_opt(z) does not require an additional spectral factorization step. The minimum-phase spectral factor H_min(z) can be obtained automatically by relating the state space realization of D_opt(z) to that of H _opt(z)     

Fast evaluation of an integral occurring in digital filteringapplications

A fast evaluation procedure for the integral I_m,n,p=1/2πj∯_|z|=1H_m,n(z)H _m,n(z^-1)z^p-1dz for arbitrary nonnegative integer-valued m, n, and p, is presented, where H_m,n (z)=Σ_k=0^mb_m,kz^-k /Σ_l=0ⁿa_n,lz^-1,a _n,0≠0 is the transfer function of an arbitrary digital filter. Evaluation of this integral frequently appears in control, communication, and digital filtering. A notable result is the one-term recursion on p, for arbitrary but fixed nonnegative integers m and n. The computational complexity is analyzed, and two illustrative examples demonstrate some of the advantages of this approach     

General Fourier solution and causality in attenuating media

It has been previously reported that a general electric field solution and its initial condition, E_g(z,t) and E_g(z,0), respectively, are not causal when formed by a superposition of time-harmonic waves in an attenuating medium. However, this is not the case. Further, the relationship between attenuation and phase velocity as well as their dependence on frequency arise simply from the form chosen for the time harmonic particular solutions. Even though causality is not introduced during the solution to the wave equation, the general solution can subsequently be shown to be a time convolution of a causal boundary condition (time history of the electric field as it crosses the z=0 plane, E_g(0,t)), and the medium's impulse response g(z,t), which can be shown to be causal. Hence, the general solution is also causal. The initial condition occurs at the instant, t=0, when the electric field arrives at the z=0 plane, and it has been previously reported that the initial condition depends on the boundary condition for times after the initial time thereby violating causality. A re-examination shows that the initial condition does not depend on times after the initial time. Hence, the initial condition obeys causality, and it can also be shown to be properly determined (E _g(z,0)=0 for z>0) even when the boundary condition is not zero. It has also been reported that limiting expressions for the boundary and initial conditions, E_g(0,t→0) and E_g (z→0,0), respectively, are not equal. However, a re-examination reveals that E_g(0,t→0)=E_g(z→0,0)     

Data fusion with minimal communication

Two sensors obtain data vectors x and y, respectively, and transmit real vectors m&oarr;₁(x) and m&oarr;₂(y), respectively, to a fusion center. The authors obtain tight lower bounds on the number of messages (the sum of the dimensions of m&oarr;₁ and m&oarr;₂) that have to be transmitted for the fusion center to be able to evaluate a given function f&oarr;(x,y). When the function f&oarr; is linear, they show that these bounds are effectively computable. Certain decentralized estimation problems can be cast in the framework and are discussed in some detail. In particular, the authors consider the case where x and y are random variables representing noisy measurements and f&oarr;(x,y)=E[z|x,y], where z is a random variable to be estimated. Furthermore, it is established that a standard method for combining decentralized estimates of Gaussian random variables has nearly optimal communication requirements     

High resolution spatial interferometry of guided optical waves

The spatial variation of the phase difference Φ(z) between collinear guided waves is measured interferometrically by scanning a localised perturbation along the guide. Milliradian phase resolution is achieved by the use of a quadrature signal. The method is demonstrated with TE⇔TM coupling in Ti:LiNbO₃. It yields the absolute value and the uniformity of the birefringence Δβ(z)=dΦ/dz     

Generic Invertibility of Multidimensional FIR Filter Banks and MIMO Systems

In this paper, we study the invertibility of M-variate Laurent polynomial N times P matrices. Such matrices represent multidimensional systems in various settings such as filter banks, multiple-input multiple-output systems, and multirate systems. Given an N times P Laurent polynomial matrix H(z₁, ..., z_M) of degree at most k, we want to find a P times N Laurent polynomial left inverse matrix G(z) of H(z) such that G(z)H(z) = J. We provide computable conditions to test the invertibility and propose algorithms to find a particular inverse. The main result of this paper is to prove that H(z) is generically invertible when N - P ges M; whereas when N - P < M, then H(z) is generically noninvertible. As a result, we propose an algorithm to find a particular inverse of a Laurent polynomial matrix that is faster than current algorithms known to us.     

On ternary complementary sequences

A pair of real-valued sequences A=(a₁,a₂,...,a_N) and B=(b₁,b ₂,...,b_N) is called complementary if the sum R(·) of their autocorrelation functions R_A(·) and R_B(·) satisfies R(τ)=R_A(τ)+R _B(τ)=Σ_i=1^N$ -^τa_ia_i+τ+Σ_j=1 ^N-τb_jb_j+τ=0, ∀τ≠0. In this paper we introduce a new family of complementary pairs of sequences over the alphabet α₃=+{1,-1,0}. The inclusion of zero in the alphabet, which may correspond to a pause in transmission, leads both to a better understanding of the conventional binary case, where the alphabet is α₂={+1,-1}, and to new nontrivial constructions over the ternary alphabet α₃. For every length N, we derive restrictions on the location of the zero elements and on the form of the member sequences of the pair. We also derive a bound on the minimum number of zeros necessary for the existence of a complementary pair of length N over α₃. The bound is tight, as it is met by some of the proposed constructions, for infinitely many lengths     

Optimal quaternary linear codes of dimension five

Let d_q(n,k) be the maximum possible minimum Hamming distance of a q-ary [n,k,d]-code for given values of n and k. It is proved that d₄ (33,5)=22, d₄(49,5)=34, d₄ (131,5)=96, d₄(142,5)=104, d₄(147,5)=108, d ₄(152,5)=112, d₄(158,5)=116, d₄(176,5)⩾129, d₄(180,5)⩾132, d₄(190,5)⩾140, d₄(195,5)=144, d₄(200,5)=148, d₄(205,5)=152, d₄(216,5)=160, d₄(227,5)=168, d₄(232,5)=172, d₄(237,5)=176, d₄(240,5)=178, d₄(242,5)=180, and d₄(247,5)=184. A survey of the results of recent work on bounds for quaternary linear codes in dimensions four and five is made and a table with lower and upper bounds for d₄(n,5) is presented     

Multivariate regression estimation of continuous-time processesfrom sampled data: local polynomial fitting approach

Let (Y,X)={Y(t),X(t),-∞j) be a renewal point processes on (0,∞), with a finite mean rate, independent of (Y,X). We consider the estimation of regression function r(x₀, x₁,...,x_m-1; τ₁,...,τ_m) of ψ(Y(τ_m)) given (X(0)=x₀, X(τ₁)=x₁,...,X(τ_m-1)=_x-1 ) for arbitrary lags 0<τ₁<...< τ_m on the basis of the discrete-time observations {Y(t_j),X(t_j),t_j)_j=1ⁿ . We estimate the regression function and all its partial derivatives up to a total order p⩾1 using high-order local polynomial fitting. We establish the weak consistency of such estimates along with rates of convergence. We also establish the joint asymptotic normality of the estimates for the regression function and all its partial derivatives up to a total order p⩾1 and provide explicit expressions for the bias and covariance matrix (of the asymptotically normal distribution)     

Theory of digital phase shifters based on high-Tcsuperconducting films

A theory of digital phase shifters based on transition from a superconducting (S) state into a normal (N) state in high-T_c superconductor (HTS) films is developed. It is shown that the insertion-loss level in the phase shifters is determined by the commutation quality of the HTS film and does not depend on the S-N switching element shape and size. The procedure for designing the S-N phase shifter with minimum insertion loss is equivalent to designing a matching circuit for the termination Z=√R_SR_N (R_S and R_N are the resistances of the switching element in the S- and N-states, respectively). Different versions of S-N phase shifters are suggested and discussed. High-quality S-N phase shifters can be successfully designed in a 1-10 GHz frequency range and find application on the receiving end of microwave systems     

Geometrical and performance analysis of GMD and Chase decodingalgorithms

The overall number of nearest neighbors in bounded distance decoding (BDD) algorithms is given by N_0,eff=N₀+N _BDD. Where NBDD denotes the number of additional, non-codeword, neighbors that are generated during the (suboptimal) decoding process. We identify and enumerate the nearest neighbors associated with the original generalized minimum distance (GMD) and Chase (1972) decoding algorithms. After careful examination of the decision regions of these algorithms, we derive an approximated probability ratio between the error contribution of a noncodeword neighbor (one of N_BDD points) and a codeword nearest neighbor. For Chase algorithm 1 it is shown that the contribution to the error probability of a noncodeword nearest neighbor is a factor of 2^d-1 less than the contribution of a codeword, while for Chase algorithm 2 the factor is 2^[d/2]-1, d being the minimum Hamming distance of the code. For Chase algorithm 3 and GMD, a recursive procedure for calculating this ratio, which turns out to be nonexponential in d, is presented. This procedure can also be used for specifically identifying the error patterns associated with Chase algorithm 3 and GMD. Utilizing the probability ratio, we propose an improved approximated upper bound on the probability of error based on the union bound approach. Simulation results are given to demonstrate and support the analytical derivations     

Silicon oxynitride and silicon oxynitride-silicon interface: aphotoemission study

A study of silicon-oxynitride materials and their interfaces with amorphous silicon using synchrotron radiation photoemission is discussed. The effect of the hydrogen atoms as an intralayer at the silicon-oxynitride-a-Si interface is also analyzed. The data relative to the bulk silicon oxynitride show that the valence band edge gradually shifts toward a higher binding energy as the [O]/[N] ratio (A) is increased. For the silicon-oxynitride-a-Si heterojunctions, the valence band discontinuities ΔE_v ranged from 1.1±0.15 eV in the case of A=0.08 up to 4.6±0.15 eV in the case of A=2.02. The effect of the hydrogen intralayer was to reduce the ΔE_v by 0.5±0.15 eV. The observed intralayer-induced effect is attributed to modification of the interface dipoles. A simple model calculation, based on electronegativity arguments, gives a reduction of 0.4 eV for A=0 and 0.46 for A corresponding to pure silicon dioxide (SiO₂)     

Switching converters with wide DC conversion range

Compared to basic converter topologies (buck, boost, buck-boost, Cuk, etc.), pulse-width modulation (PWM) converters with quadratic DC conversion ratios, M(D)=D², M (D)=D²/(1-D) or M(D)=D²/(1-D)² , offer a significantly wider conversion range. For a given minimum ON-time and, consequently, for a given minimum duty ratio D _min, D² in the numerator of M (D) yields a much lower limit on the minimum attainable conversion ratio. By applying a systematic synthesis procedure, six novel single-transistor converter configurations with quadratic DC conversion ratios are found. The simpler, single-transistor realization is the most important advantage over the straightforward cascade of two basic converters. As far as conversion efficiency is concerned, it is clear that a single-stage converter is usually a better choice than a two-stage converter. The quadratic converters proposed are intended for applications where conventional single-stage converters are inadequate-for high-frequency applications where the specified range of input voltages and the specified range of output voltages call for an extremely large range of conversion ratios     

A general combinatorial sphere decoder and its application

The conventional problem of searching the shortest vector z of a N-dimensional lattice L(H) with generating matrix HisinR^NtimesM is considered in a more general setting. There are P generating matrices H_iisinR^NtimesM(i=1,2,...,P) of the P lattices L(H_i). For a (bounded) integer vector bisinZ^M , we obtain P lattice points H_ib. Let d_i be the Euclidean norm of H_ib. The problem of interest is how to search for a vector b so that the maximum of d_i is minimized. We propose a new sphere decoder called combinatorial sphere decoder (CSD) to solve this problem. One of the applications of the new CSD is presented in detail to show its effectiveness     

MMSE decision-feedback equalizers and coding. II. Coding results

For pt.I see ibid., vol.43, no.10, p.2582 (1995). The minimum-mean-squared-error decision-feedback equalizer (MMSE-DFE) has properties that suggest that it is a canonical equalization structure in systems that combine equalization with coded modulation. With a given symbol rate 1/T and transmit spectrum, the output signal-to-noise ratio SNR_MMSE-DFE,U of a MMSE-DFE with an unbiased decision rule is a single parameter that characterizes the channel for coding purposes. Indeed, the transmit spectrum that maximizes SNR_MMSE-DFE,U is the capacity-achieving (water-pouring) spectrum, and the capacity C(T) (in bits per two dimensions) is given by C(T)=log₂[1+SNR_MMSE-DFE,U] regardless of the channel characteristics. The performance of a coded system with a MMSE-DFE equalization structure may be accurately estimated using the gain of the coding scheme at a given Pr(E). This performance is shown to be approximately the same as that of a multicarrier system using the same transmit spectrum and similar coding; such systems are known to be able to approach capacity arbitrarily closely. The MMSE-DFE can perform significantly better than a zero-forcing decision-feedback equalizer, particularly at moderate-to-low SNR's and on severe-ISI channels. Simulation results indicate that performance of the MMSE-DFE is surprisingly insensitive to transmit spectral shaping, as long as the transmit spectrum exceeds the capacity-achieving band, but that there is an optimal symbol rate that should (approximately) be used     

T(z) diagram and optical energy gap values of Cd1−zMnzGa2Se4 alloys

The T(z) diagram of the system Cd_1−zMn_zGa₂Se₄ was obtained from x-ray diffraction and differential thermal analysis measurements. It was found that at lower temperatures, a single phase solid solution occurs across the whole compositional range and values of lattice parameters were determined as a function of z. At higher temperatures, an order-disorder transition occurs, in the range 0 < z < 0.6 to a partially ordered tetragonal structure and for 0.6 < z < 1. 0 to a disordered defect zinc-blende structure. In the T(z) diagram, both the ordering boundary and the solidus curve appear to show discontinuities at z = 0.6, corresponding to the change in the disordered phase. It is suggested that the symmetries of the terminal compounds are different one from the other. Optical absorption measurements were made at 300 K to show the variation of the direct optical energy gap E_o with z, and again the values appear to divide into two parts below the above z = 0.6.     

Improved L2-sensitivity for state-space digital system

An improved L₂-sensitivity measure for linear state-space digital systems is presented. It gives a more precise evaluation of the transfer function deviation ΔH(z) between the infinite wordlength system and the finite wordlength system when the structure matrices {A,b,c} contain 0 and ±1 coefficients. This measure can be applied in the system optimization, resulting in a computationally efficient and very low L₂-sensitivity structure. The theoretical result is verified by a numerical example     

Dielectric constant measurements of finite-size sheet at microwavefrequencies by pseudo-Brewster's angle method

Dielectric constant (ϵ_r) measurements for finite-size dielectric sheets (DS's) at centimeter wavelengths are presented using the method-of-measuring pseudo-Brewster's angle. This method is applied to measure ϵ_r of sheets of Plexiglas and window glass. In the experiment, two horn antennas are used to transmit and receive p-polarized waves. A dielectric sheet is located between the two antennas and rotated 180°, which produces two peaks in the transmittance curves. For a more accurate measurement of Brewster's angle, an optical spectrometer with 1-min accuracy is also used. By this method, ϵ_r of Plexiglas and window glass are obtained to be 2.55±0.13 and 5.35±0.1, respectively. This method measures |ϵ_r|, but the measurement is easy and nondestructive for DS's. Finally, an accurate method of error calculation is used to calculate the error in the measured values of ϵ_r     

Analytical design of 3-D wavelet filter banks using themultivariate Bernstein polynomial

The design of 3-D multirate filter banks where the downsampling/upsampling is on the FCO (face centred orthorhombic) lattice is addressed. With such a sampling lattice, the ideal 3-D sub-band of the low-pass filter is of the TRO (truncated octahedron) shape. The transformation of variables has been shown previously to be an effective technique for designing M-D (multidimensional) filter banks. A design technique is presented for the transformation function using the multivariate Bernstein polynomial which provides a good approximation to the TRO sub-band shape. The method is analytically based and does not require any optimisation procedure. Closed form expressions are obtained for the filters of any order. Another advantage of this technique is that it yields filters with a flat frequency response at the aliasing frequency (ω₁, ω₂ , ω₃)=(π, π, π). This flatness is important for giving regular discrete wavelet transform systems     

Temperature sensitivity of phase-matched second-harmonic generationin LiIO3

Measurements were made of the temperature dependence (between 23 and 65°C) of the phase-matching angle &thetas;_pm for type I frequency doubling of 1064-nm laser light in lithium iodate (LiIO₃). The measured value of d&thetas;_pm/dT is -14.7±1 μrad/°C, which corresponds to a thermal sensitivity β_T =0.24±0.02 cm^-1/°C for this process. Also calculated is a value of d&thetas;_pm/dT using experimentally determined thermooptic data available in the literature. The calculated value of d&thetas;_pm/dT is -31±18 μrad/°C using literature values of n and dn/dT for LiIO₃. The extreme sensitivity of the calculated value of d&thetas;_pm/dT to small errors in the thermooptic coefficients may be the reason for this discrepancy