The Zak transform and some counterexamples in time-frequencyanalysis

It is shown how the Zak transform can be used to find nontrivial examples of functions f, g∈L²(R) with f×g≡0≡F×G, where F, G are the Fourier transforms of f, g, respectively. This is then used to exhibit a nontrivial pair of functions h, k∈L²(R), h≠k, such that |h|=|k|, |H |=|K|. A similar construction is used to find an abundance of nontrivial pairs of functions h, k∈L² (R), h≠k, with |A_h |=|A_k| or with |W_h|=|W _k| where A_h, A_k and W_h, W_k are the ambiguity functions and Wigner distributions of h, k, respectively. One of the examples of a pair of h, k∈L²(R), h≠k , with |A_h|=|A_k| is F.A. Grunbaum's (1981) example. In addition, nontrivial examples of functions g and signals f₁≠f₂ such that f₁ and f₂ have the same spectrogram when using g as window have been found     

Optimality property of the Gaussian window spectrogram

It is shown that for any signal x(t) the minimum of ∫_-∞^∞∫_-∞ ^∞ [(t-t_x)²+(f-f _x)²] S_x^(w)(t , f) dt df over all normalized time-windows w(t) is achieved by the Gaussian window w(t)=2^1/4 exp (-πt²). Here (t_x, f _x) is the center of gravity of the signal x(t ), S_x^(w) (t, f) is the spectrogram of x(t) due to the window w( t), and the double integral is a measure of the spread of S _x^(w) (t, f) around (t _x, f_X) in the time-frequency plane     

Effect of conduction-band discontinuity on lasing characteristicsof 1.5 μm InGaAs/In(Ga)AlAs MQW-FP lasers

The characteristic temperature (T₀), relaxation frequency (f_r), differential gain (dg /dn) and nonlinear gain coefficient (ϵ) of 1.5-μm InGaAs/In(Ga)AlAs multiple-quantum-well (MQW) Fabry-Perot (FP) lasers grown by gas source molecular beam epitaxy (GSMBE) are reported. It is found that T₀ is little affected by the difference in the conduction band discontinuity. A maximum T₀ value of 86 K is obtained. The dg/dn and ϵ∈ were calculated from the slope of the f_r versus √ power plot and the damping K-factor. It is demonstrated that dg/dn and ϵ of InGaAs/In(Ga)AlAs MQW lasers increase with an increase in the conduction band discontinuity     

Optimal data-based kernel estimation of evolutionary spectra

Complex demodulation of evolutionary spectra is formulated as a two-dimensional kernel smoother in the time-frequency domain. First, a tapered Fourier transform, y_v(f, t), is calculated. Then the log-spectral estimate, is smoothed. As the characteristic widths of the kernel smoother increase, the bias from the temporal and frequency averaging increases while the variance decreases. The demodulation parameters, such as the order, length, and bandwidth of spectral taper and the kernel smoother, are determined by minimizing the expected error. For well-resolved evolutionary, spectra, the optimal taper length is a small fraction of the optimal kernel halfwidth. The optimal frequency bandwidth, w, for the spectral window scales as w²~λ/τ, where τ is the characteristic time and λ_F is the characteristic frequency scalelength. In contrast, the optimal halfwidths for the second stage kernel smoother scales as h~1/(τλ_F )¹(p+2)/ where p is the order of the kernel smoother. The ratio of the optimal-frequency halfwidth to the optimal-time halfwidth is determined     

InGaAs/InAlAs/InP collector-up microwave heterojunction bipolartransistors

Collector-up InGaAs/InAlAs/InP heterojunction bipolar transistors (HBTs) were successfully fabricated, and their DC and microwave characteristics measured. High collector current density operation (J_c>30 kA/cm²) and high base-emitter junction saturation current density (J₀>10^-7 A/cm²) were achieved. A cutoff frequency of f _t=24 GHz and a maximum frequency of oscillation f _max=20 GHz at a collector current density of J₀ =23 kA/cm² were achieved on a nominal 5-μm×10-μm device     

Correlation between 1/f noise and hFElong-term instability in silicon bipolar devices

Accelerated life tests with high-temperature storage and electric aging for n⁺-p-n silicon planar transistors were carried out. Current gain h_FE increases monotonously with time during the tests, and the h_FE drift is correlated with initial measured 1/f noise in the transistors, i.e. the drift amount significantly increases with the increase of noise level. The correlation coefficient of relative drift Δh_FE /h_FE and 1/f noise spectral density S_iB(f) is far larger than that of Δ h_FE/h_FE and initial DC parameters of the transistors. A quantitative theory model for the h _FE drift has been developed and explains the h _FE drift behavior in the tests, which suggests that the h _FE drift and 1/f noise can be attributed to the same physical origin, and both are caused by the modulation of the oxide traps near the Si-SiO₂ interface to Si surface recombination. 1/f noise measurement, therefore, may be used as a fast and nondestructive means to predict the long-term instability in bipolar transistors     

A strengthening of the Assmus-Mattson theorem

Let w₁=d,w₂,…,w _s be the weights of the nonzero codewords in a binary linear [n,k,d] code C, and let w' ₁, w'₂, …, w'₃, be the nonzero weights in the dual code C1. Let t be an integer in the range 0<t<d such that there are at most d-t weights w'_i with 0<w'_i ⩽n-t E. F. Assmus and H. F. Mattson, Jr. (1969) proved that the words of any weight w_i in C form a t-design. The authors show that if w₂⩾d+4 then either the words of any nonzero weight w_i form a (t+1)-design or else the codewords of minimal weight d form a {1,2,…,t,t+2}-design. If in addition C is self-dual with all weights divisible by 4 then the codewords of any given weight w_i form either a (t +1)-design or a {1,2,…,t,t+2}-design. The proof avoids the use of modular forms     

The axisymmetric modes in a longitudinal inhomogeneous SELFOC fiber

The authors consider the propagation characteristics and mode conversion of axisymmetric modes in an imperfect SELFOC fiber with longitudinal gradually varying dielectric constant K=ϵ/ϵ₀=K₀-K ₂(z)r². An analytic solution which is expressed in terms of generalized Laguerre polynomials is found     

Quarter-micrometer gate ion-implanted GaAs MESFET's with an f1 of 126 GHz

The fabrication and characterization of a 0.25-μm-gate, ion-implanted GaAs MESFET with a maximum current-gain cutoff frequency f_t of 126 GHz is reported. Extrapolation of current gains from bias-dependent S-parameters at 70-100% of I _dss yields f₁'s of 108-126 GHz. It is projected that an f₁ of 320 GHz is achievable with 0.1-μm-gate GaAs MESFETs. This demonstration of f₁'s over 100 GHz with practical 0.25-μm gate length substantially advances the high-frequency operation limits of short-gate GaAs MESFETs     

Molecular-beam growth of homoepitaxial InSb photovoltaic detectors

Molecular-beam epitaxy has been used for the first time to fabricate np junctions in InSb grown onto p-type InSb (100) substrates. Diodes formed by the epitaxial growth of a silicon-doped layer on undoped homoepitaxial material exhibited a bulk generation-recombination-limited R₀A value of 10⁵ Ω cm² and D_λpk * of 3×10¹² cm Hz^1/2 W^-1 at liquid nitrogen temperature     

Longitudinal and transverse current distributions on coupledmicrostrip lines

The normalized longitudinal and transverse current distributions on coupled microstrip lines are obtained for even and odd modes by using the charge conservation formula and the charge distributions calculated by a Green's function technique. Their dependence on the shape ratios w/h and s/h and on the relative permittivity ε* of the substrate is shown     

Design of lightweight, broad-band microwave absorbers using geneticalgorithms

A procedure for synthesizing multilayered radar absorbing coatings is presented. Given a predefined set of N_m available materials with frequency-dependent permittivities ∈_i(f) and permeabilities μ_i(f ) (i=1,. . ., N_m), the technique determines simultaneously the optimal material choice for each layer and its thickness. This optimal choice results in a screen which maximally absorbs TM and TE incident plane waves for a prescribed range of frequencies {f₁,f₂,. . ., f _Nf} and incident angles {&thetas;₁, &thetas;₂,. . .,&thetas;_N&thetas;}. The synthesis technique is based on a genetic algorithm. The technique automatically places an upper bound on the total thickness of the coating, as well as the number of layers contained in it, which greatly simplifies manufacturing. In addition, the thickness or surface mass of the coating can be minimized simultaneously with the reflection coefficient. The algorithm was successfully applied to the synthesis of wideband absorbing coatings in the frequency ranges of 0.2-2 GHz and 2-8 GHz     

Capacity of the Gaussian arbitrarily varying channel

The Gaussian arbitrarily varying channel with input constraint Γ and state constraint Λ admits input sequences x=(x₁,---,X_n) of real numbers with Σx_i²⩽nΓ and state sequences s=(S₁,---,s_n ) of real numbers with Σs_i²⩽nΛ; the output sequence x+s+V, where V=(V₁,---,V_n) is a sequence of independent and identically distributed Gaussian random variables with mean 0 and variance σ². It is proved that the capacity of this arbitrarily varying channel for deterministic codes and the average probability of error criterion equals 1/2 log (1+Γ/(Λ+σ²)) if Λ<Γ and is 0 otherwise     

Tests of microstrip dispersion formulas

A set of published formulas for the frequency dependence of the microstrip effective relative dielectric constant ϵ_re( f) is tested relative to an assemblage of measured data values for this quantity chosen from the literature. The RMS deviation of the predicted data obtained from the measured values ranged from 2.3% to 4.1% of the seven formulas for ϵ_re(f) tested. A formula due to M. Kirschning and R.H. Jansen (see Electron. Lett., vol.18, p.272-73, 1982) showed the lowest average deviation from measured values, although the differences between the predictions of their formula and others tested are of the order of the error limits of the comparison process. It is concluded that the results indicate the suitability of relatively simple analytical expressions for the computation for microstrip dispersion     

Si/a-Si:H heterojunction microwave bipolar transistors with cut-offfrequencies ft above 5 GHz

The fabrication of a silicon heterojunction microwave bipolar transistor with an n⁺ a-Si:H emitter is discussed, and experimental results are given. The device provides a base sheet resistance of 2 kΩ/□ a base width 0.1 μm, a maximum current gain of 21 (V_CE=6 V, I_c=15 mA), and an emitter Gummel number G _E of about 1.4×10¹⁴ Scm^-4. From the measured S parameters, a cutoff frequency f_t of 5.5 GHz and maximum oscillating frequency f_max of 7.5 GHz at V_CE=10 V, I_c=10 mA are obtained     

Monte Carlo studies of the effect of emitter junction grading onthe electron transport in InAlAs/InGaAs heterojunction bipolartransistors

InAlAs/InGaAs HBTs with various emitter junction gradings are simulated using a self-consistent Monte Carlo simulator. The effects of the emitter junction grading and the shift of the emitter-base p-n junction into the emitter depletion region due to diffusion of the base dopant are investigated. A minimum transit time of 1.18 ps is predicted for an In(Ga_1-xAl_x)As grading with x=0.6 at the E-B interface and J_C=0.7×10⁵ A/cm². Graded-base designs do not offer any transit time performance improvement compared with the graded E-B approach. For transient performance, the device switching time is found to remain constant at about 2.2 ps up to x₀~0.7 but increases for larger values. A cutoff frequency as high as 270 GHz was observed for x₀=0.7, indicating that the best transport can be achieved from intermediately graded rather than abrupt E-B junction designs     

A high-performance lateral bipolar transistor fabricated on SIMOX

Double-diffused, lateral n-p-n bipolar transistors were fabricated in a simple CMOS-like process using SIMOX silicon-on-insulator (SOI) substrates. Excellent device characteristics were achieved, with peak h_FE=120, BV_CEO=10 V, and peak f_t=4.5 GHz. The f_t versus BV _CEO trade-off was studied as a function of n ^- collector width. f_t>25 GHz is predicted for this structure with an improved device layout and optimized basewidth. This process may be easily extended in order to fabricate complementary BJTs in a C-BiCMOS thin-film SOI technology     

On the number of memories that can be perfectly stored in a neuralnet with Hebb weights

Let {w_ij} be the weights of the connections of a neural network with n nodes, calculated from m data vectors v¹, ···, v^m in {1,-1}ⁿ, according to the Hebb rule. The author proves that if m is not too large relative to n and the v^k are random, then the w_ij constitute, with high probability, a perfect representation of the v^k in the sense that the v ^k are completely determined by the w_ij up to their sign. The conditions under which this is established turn out to be less restrictive than those under which it has been shown that the v^k can actually be recovered by letting the network evolve until equilibrium is attained. In the specific case where the entries of the v^k are independent and equal to 1 or -1 with probability 1/2, the condition on m is that m should not exceed n/0.7 log n     

Pulse dispersion distortion in open and shielded microstrips usingthe spectral-domain method

The spectral-domain method is used to compute the effective dielectric constant [ϵ_r/_eff(f)] of open and shielded microstrip lines to analyze the dispersion distortion of short electrical pulses. Precise expressions for the longitudinal and transverse current distributions allow a high level of accuracy for ϵ_r/_eff(f). It is determined that computation time can be minimized for the open microstrip calculations by using the shielded microstrip formulation provided large dimensions for the conducting walls are assumed     

Measurement of the characteristics of the optical-microwavedouble-resonance effect of the 87Rb D1line for application as an atomic frequency standard

The OMDR (optical-microwave double resonance) spectrum of ⁸⁷ Rb with the aim of using a frequency-stabilized GaAs semiconductor laser instead of an Rb lamp as a pumping source in a gas-cell-type Rb frequency standard. Natural isotope ⁸⁷Rb was sealed in a glass cell with buffer gases (Ar/N₂=1.2, total pressure=39 torr). The double resonance signal in the 5P_1/2(F=2)←5S_1/2( F=1) transition appearing at the resonance to the F=2←1 hyperfine transition of the 5S_1/2 state was detected. The optimum operational cell temperature was 56°C. The peak-to-peak frequency width of the atomic hyperfine resonance discriminator used to stabilize the microwave frequency shifts induced by detuning of the laser frequency, changes in the laser and microwave powers, and temperature drift of the cell were investigated