Recursive Halfband-Filters

The paper describes the properties and the design of recursive halfband-filters.The two possibilities of being complementary are introduced. The lowpass with the transfer function H_Lp(z)and the corresponding highpass, described by H_Hp(z) = H_Lp(-z)can either be strictly complementary or power complementary. According to the respective symmetry, the impulse responses, transfer functions and frequency responses possess certain characteristic properties, which are described in section 2. It turns out that these resulting symmetries of the frequency response reduce the number of the choosable design parameters. We can only prescribe the cutoff frequency and the tolerated deviation either for the passband or the stopband.

In the third section we treat the design of halfband-filters with approximately linear phase. By coupling an appropriately designed allpass of even degree n_A with a delay of order m=n_A±1 we obtain the desired solution by solving a corresponding approximation problem for the phase of the allpass. The resulting lowpass and highpass are strictly as well as power complementary!The kind of approximation will be done in the sense of maximal flatness, where a closed form solution exists [8], or in the sense of Chebychev, where the solution is obtained iteratively [13]. The design of systems with minimum phase is presented in section 4. The resulting lowpass and highpass are power complementary. Closed form solutions yield Butterworthand Cauer filters, if a maximal flat or a Chebychev approximation is desired. In all cases a fixed relation exists between the passband frequency Ω_P and the tolerated deviation δ_P in the passband when the degree n has been chosen.     

Profiling Voids Embedded in a Slab by a Non-Linear Model

In this paper, by applying a non linear model for the electromagnetic inverse scattering, a technique for the dielectric profiling of a planarly layered medium is investigated and applied to void localization and diagnostics inside a homogeneous lossless slab (one-dimensional geometry). Data are collected under plane wave multifrequency normal incidence. Suitable finite dimensional representations for the unknown functions are introduced and their influence on the model is discussed. The resulting functional equation is solved by the method of weighted residuals and the solution algorithm amounts to minimizing a non quadratic function, where particular attention is devoted to reduce the occurrence of local minima. Finally, the inversion algorithm is validated by applications to both simulated and experimental data.     

Optimal fault margin in a computer system

This paper suggests a stochastic model how to determine a fault margin in a computer system, who fails when the total number of hidden faults exceeds a threshold level N of tolerance: A fault occurs at a non-homogeneous Poisson process, and (i) becomes system failure with probability p₁, (ii) becomes hidden fault with probability p₂ and is accumulated, or (iii) is removed with probability p₃. The expected cost rate to system failure is derived, and an optimal number N^* to minimize it is discussed. A numerical example is finally given.     

Temperature analysis and characteristics of highly strainedInGaAs-GaAsP-GaAs (λ > 1.17 μm) quantum-well lasers

Characteristic temperature coefficients of the threshold current (T₀) and the external differential quantum efficiency (T₁) are studied as simple functions of the temperature dependence of the physical parameters of the semiconductor lasers. Simple expressions of characteristic temperature coefficients of the threshold current (T₀) and the external differential quantum efficiency (T₁) are expressed as functions as physical parameters and their temperature dependencies. The parameters studied here include the threshold (J_th) and transparency (J_tr ) current density, the carrier injection efficiency (η_inj ) and external (η_d) differential quantum efficiency, the internal loss (α_i), and the material gain parameter (g_o). The temperature analysis is performed on low-threshold current density (λ = 1.17-1.19 μm) InGaAs-GaAsP-GaAs quantum-well lasers, although it is applicable to lasers with other active-layer materials. Analytical expressions for T ₀ and T₁ are shown to accurately predict the cavity length dependence of these parameters for the InGaAs active lasers     

Temperature-dependent Sellmeier coefficients and chromaticdispersions for some optical fiber glasses

Temperature-dependent Sellmeier coefficients are necessary to optimize optical design parameters of the optical fiber transmission system. These coefficients are calculated for fused silica (SiO₂ ), aluminosilicate, and Vycor glasses for the first time to find the temperature dependence of chromatic dispersion at any wavelength from UV to 1.7 μm. The zero dispersion wavelength λ₀ (1.273 μm for SiO₂, 1.393 μm for aluminosilicate, and 1.265 μm for Vycor glasses at 26°C) varies linearly with temperature, and dλ₀/dT is 0.03 nm/K for aluminosilicate and Vycor glasses, whereas for SiO₂ it is 0.025 nm/K. This study interprets the recently observed experimental value of dλ₀/dT for two dispersion shifted optical fibers; and the dominantly material origin of dλ₀/dT is confirmed here as a fundamental property of the optical fiber glasses     

Analysis of Serial and Hybrid Concatenated Space-Time Codes Applying Iterative Decoding

In this letter, we investigate serial and hybrid concatenated space-time (SC-ST and HC-ST) codes applying iterative decoding topologies. The coding operations are based on the concatenation of convolutional coding, interleaving, and space-time coding along with a multiple-transmitter/multiple-receiver diversity system. Through the analysis of the SC-ST and HC-ST coding systems, improved design specifications can be selected for the component encoders with considerations of the wireless channel characteristics. Based on the iterative decoding process and the optimum parameter selection operations, a considerable improvement in the error rate performance is obtained. For the applied specs, the results indicate that at the frame error rate (FER) 10⁻² level the SC-ST coding system provides a coding gain of approximately 3 dB in comparison to the Tarokh, Seshadri, Calderbank (TSC) space-time (ST) code [1], where the HC-ST coding system provides an additional coding gain of approximately 1 dB beyond the SC-ST code.     

H∞ filtering of 2-D discrete systems

This paper deals with H_∞ filtering of two-dimensional (2-D) linear discrete systems described by a 2-D local state-space (LSS) Fornasini-Marchesini (1978) second model. Several versions of the bounded real lemma of the 2-D discrete systems are established. The 2-D bounded real lemma allows us to solve the finite horizon and infinite horizon H_∞ filtering problems using a Riccati difference equation or a Riccati inequality approach. Further a solution to the infinite horizon H_∞ filtering problem based on a linear matrix inequality (LMI) approach is developed. Our results extend existing work for one-dimensional (1-D) systems to the 2-D case and give a state-space solution to the bounded realness of 2-D discrete systems as well as 2-D H_∞ filtering for the first time. Numerical examples are given to demonstrate the Riccati difference equation approach to the 2-D finite horizon H_∞ filtering problem and the LMI approach to the 2-D infinite horizon H_∞ filtering problem     

Optically detected impurity D and D transitions in GaAs quantum wells

We have carried out a far-infrared magnet-optical study on shallow donor states confined in GaAs quantum wells (QWs), applying a recently developed optical detection technique. We have observed, in addition to cyclotron resonance, the 1s → 2p₊ transition of neutral donors (D⁰), and singlet and triplet transitions of negative donor ions (D⁻); the latter observation verifies the existence of D⁻ ions in well-only doped QWs under optical pumping. This is the first observation of optically detected impurity resonances in confined systems and demonstrates the power and utility of this technique for such studies.     

Parametrized Family of 2-D Non-factorable FIR Lossless Systems and Gröbner Bases

The factorability of one-dimensional (1-D) FIR lossless transfer matrices [1] in terms of Givens rotations produces the parameters that can be used for an optimal design of filter banks with prespecified filtering characteristics. Two dimensional (2-D) FIR lossless systems behave quite differently, however. Venkataraman-Levy [2] and Basu-Choi-Chiang [3] have constructed 2-D FIR paraunitary matrices of McMillan degrees (2,2) that are not factorable. Because of the state-space realization used in the construction, they are floating-point approximations, and they do not produce explicit parametrizations that can be used for optimal design process. In this paper, we formulate the lossless condition and nonfactorability condition of a 2-D FIR paraunitary matrix using multivariate polynomials in the coefficients. The resulting polynomial system can be explicitly solved with Gröbner bases. By studying the polynomial system, we obtain a continuous one parameter family of 2-D 2×2 non-factorable paraunitary matrices. As an example, we get a closed-form expression for a 2-D 2×2 paraunitary matrix that is not factorable into rotations and delays.     

Design of Sigma–Delta Modulators With Arbitrary Transfer Functions

This paper addresses the design of sigma-delta modulators with arbitrary signal and noise transfer functions using a genetic algorithm (GA)-based search method. The objective function is defined to include the difference D between the magnitude of the frequency responses of the designed transfer functions and the ideal one, the quantizer gain lambda_critical for which the poles of the modulator start moving out of the unit circle, and the spread of the coefficients S. Stability can be improved by reducing lambda_critical while a smaller S reduces the implementation complexity. A GA searches for poles/zeros of the transfer functions to minimize the objective function D+w₁*lambda_critical+w₂*S, where w₁ and w₂ are two weighing factors. Numerical results demonstrate the effectiveness of the proposed method     

Electron-optical-phonon scattering in the emitter and collector barriers of semiconductor-metal-semiconductor structures

A theoretical analysis is made of the effects on the emitter-collector current transfer ratio of optical-phonon scattering of electrons in the emitter and collector semiconductors of semiconductor-metal-semiconductor structures. The collector and emitter efficiencies are shown to increase appreciably with increasing collector and emitter electric fields respectively. At temperatures such that kT ≈ the optical-phonon energy, E₀, the collector efficiency varies only slightly with increasing emitter-collector barrier height difference, Δ, but the emitter efficiency is greatly decreased when Δ<E₀. The collector and emitter efficiencies increase substantially with decreasing temperature when Δ<E₀, but only slightly when Δ>E₀.

The current transfer ratios predicted by this theory for Si---Au---Si and GaAs---Au---Si structures are 0·68 and 0·55 respectively at 298°K and 0·85 and 0·61 respectively at 105°K with a collector field of 10⁵ V/cm. This calculation does not treat collisions in the metal or quantum-mechanical reflection of electrons at the collector barrier.     

Block 2-D interpolation, efficient matrix factorization andapplication to signal processing

A block 2-D decomposition and a new block LU matrix factorization based on a Newton approach are presented for solving quickly and efficiently polynomial or exponential 2-D interpolation problems. The sample grids under consideration are described by the product representation {x₀, x₁, . . ., x_n} x{y₀, y ₁, . . ., y_m}, where the x grid and the y-grid are not necessarily uniformly spaced. The attractive features of the method are the inherent efficient parallelism, the reduced computational requirements needed for the LU decomposition, and the capability of implementation of 1-D fast and accurate algorithms. The proposed method can be used for modeling 2-D discrete signals, designing 2-D FIR filters, 2-D Fourier matrix factorization, 2-D DFT, etc     

On the fast approximation of Green's functions in MPIE formulationsfor planar layered media

The numerical implementation of the complex image approach for the Green's function of a mixed-potential integral-equation formulation is examined and is found to be limited to low values of κ_oρ (in this context κ₀ρ = 2πρ/λ₀, where ρ is the distance between the source and the field points of the Green's function and λ₀ is the free space wavelength). This is a clear limitation for problems of large dimension or high frequency where this limit is easily exceeded. This paper examines the various strategies and proposes a hybrid method whereby most of the above problems can be avoided. An efficient integral method that is valid for large κ₀ρ is combined with the complex image method in order to take advantage of the relative merits of both schemes. It is found that a wide overlapping region exists between the two techniques allowing a very efficient and consistent approach for accurately calculating the Green's functions. In this paper, the method developed for the computation of the Green's function is used for planar structures containing both lossless and lossy media     

A suboptimal lossy data compression based on approximate patternmatching

A practical suboptimal (variable source coding) algorithm for lossy data compression is presented. This scheme is based on approximate string matching, and it naturally extends the lossless Lempel-Ziv (1977) data compression scheme. Among others we consider the typical length of an approximately repeated pattern within the first n positions of a stationary mixing sequence where D percent of mismatches is allowed. We prove that there exists a constant r₀(D) such that the length of such an approximately repeated pattern converges in probability to 1/r₀(D) log n (pr.) but it almost surely oscillates between 1/r_-∞(D) log n and 2/r₁(D) log n, where r _-∞(D)>r₀(D)>r₁(D)/2 are some constants. These constants are natural generalizations of Renyi entropies to the lossy environment. More importantly, we show that the compression ratio of a lossy data compression scheme based on such an approximate pattern matching is asymptotically equal to r₀(D). We also establish the asymptotic behavior of the so-called approximate waiting time N_l which is defined as the time until a pattern of length C repeats approximately for the first time. We prove that log N_l/l→r₀(D) (pr.) as l→∞. In general, r₀(D)>R(D) where R(D) is the rate distortion function. Thus for stationary mixing sequences we settle in the negative the problem investigated by Steinberg and Gutman by showing that a lossy extension of the Wyner-Ziv (1989) scheme cannot be optimal     

Avalanche breakdown voltage of GaAs hyperabrupt junctions

The avalanche breakdown voltage of a GaAs hyperabrupt junction diode is calculated by using unequal ionization rates for electrons and holes, and shown graphically as a function of the parameters which characterize the impurity profile of the diode. The breakdown voltage decreases abruptly at the critical point of the characteristic length L_c which varies in accordance with the impurity concentration N₀ at X = 0. For example, the critical length L_c is 7.7 × 10⁻⁶ cm and 3.3 × 10⁻⁵ cm for N₀ = 1 × 10¹⁸ cm⁻³ and 1 × 10¹⁷ cm⁻³, respectively. The breakdown voltage of a diode with extremely short or long characteristic length can be estimated from the results for corresponding abrupt junctions. The experimental results agree well with the calculated ones.     

Network theory without circuit elements

Network methods are by no means limited to lumped systems. Once the ports of a generalized physical structure are defined by use of a modal decomposition of signals, the structure can be analyzed using network techniques which extend beyond the domain of RLC systems and rational network functions. If the physical system is observed as a black box at its ports and various physical time-domain postulates such as linearity, energy, and power conservation theorems are applied in network terms, a variety of realizability relations are obtained for linear, passive, time-invariant structures. For example, one is led to generalizations of bounded real and positive real functions for distributed systems. The network technique also results in a number of interesting theorems for lossless structures such as a generalization of Foster's reactance theorem, and restrictions on minimum phase realizability, and on signal transmission and group delay in distrributed, lossless networks. These results apply in structures containing gyrotropic, dispersive media as well as in the reciprocal, nondispersive case.     

Uncertainty inequalities for linear canonical transform

The novel Hausdorff-Young inequalities associated with the linear canonical transform (LCT) are derived based on the relation between the Fourier transform and the LCT in p-norm space (0<pa, b, c, d). Meanwhile, from the uncertainty relation for Shannon entropy the Heisenberg's uncertainty relation in LCT domains is derived, which holds for both real and complex signals. Moreover, the Heisenberg's uncertainty principle for the windowed fractional Fourier transform is obtained. Finally, one review of the uncertainty relations for the LCT and other transforms is listed in tables systematically for the first time.     

Spectral factorization of two-variable para-Hermitian polynomial matrices

This paper presents an algorithm for the so-called spectral factorization of two-variable para-Hermitian polynomial matrices which are nonnegative definite on thej axis, arising in the synthesis of two-dimensional (2-D)passive multiports, Wiener filtering of 2-D vector signals, and 2-D control systems design. First, this problem is considered in the scalar case, that is, the spectral factorization of polynomials is treated, where the decomposition of a two-variable nonnegative definite real polynomial in a sum of squares of polynomials in one of the two variables having rational coefficients in the other variable plays an important role (cf. Section 4). Second, by using these results, the matrix case can be accomplished, where in a first step the problem is reduced to the factorization of anunimodular para-Hermitian polynomial matrix which is nonnegative definite forp=j , and in a second step this simplified problem is solved by using so-called elementary row and column operations which are based on the Euclidian division algorithm. The matrices considered may be regular or singular and no restrictions are made concerning the coefficients of their polynomial entries; they may be either real or complex.     

Fast computation of the two-dimensional generalised Hartleytransforms

The two-dimensional generalised Hartley transforms (2-D GDHTs) are various half-sample generalised DHTs, and are used for computing the 2-D DHT and 2-D convolutions. Fast computation of 2-D GDHTs is achieved by solving (n₁+(n₀₁/2))k₁+(n₂+(n₀₂ /2))k₂=(n+(½))k mod N, n₀₁, n₀₂ =1 or 0. The kernel indexes on the left-hand side and on the right-hand side belong to the 2-D GDHTs and the 1-D H₃, respectively. This equation categorises N×N-point input into N groups which are the inputs of a 1-D N-point H₃. By decomposing to 2-D GDHTs, an N×N-point DHT requires a 3N/2ⁱ 1-D N/2ⁱ-point H₃, i=1, ..., log₂N-2. Thus, it has not only the same number of multiplications as that of the discrete Radon transform (DRT) and linear congruence, but also has fewer additions than the DRT. The distinct H ₃ transforms are independent, and hence parallel computation is feasible. The mapping is very regular, and can be extended to an n-dimensional GDHT or GDFT easily