Some cross correlation properties for distorted signals

For a nondecreasing distortion characteristicphi(cdot)and a given signalx(cdot), the "cross correlation" function defined byR_{phi} (tau) triangleq int_{-infty}^{infty} phi[x(t)]x(t - tau) dtis shown to satisfy the inequalityR_{phi}(tau) leq R_{phi}(0), for alltau, generalizing an earlier result of Richardson that requiredphi(cdot)to be continuous and strictly increasing. The methods of the paper also show that, under weak conditions, begin{equation} R_{phi,psi}(tau) triangleq int_{-infty}^{infty} phi[x(t)]psi[x(t - tau)] dt leq R_{phi,psi}(0) end{equation} whenpsiis strictly increasing andphiis nondecreasing. In the case of hounded signals (e.g., periodic functions), the appropriate cross correlation function is begin{equation} mathcal{R}_{phi,psi}(tau} triangleq lim_{T rightarrow infty} (2T)^{-l} int_{-T}^T phi[x(t)]psi[x(t - tau)] dt. end{equation} For this case it is shown thatmathcal{R}_{phi,psi} (tau) leq mathcal{R}_{phi,psi}(0)for any nondecreasing (or nonincreasing) distortion functionsphiandpsi. The result is then applied to generalize an inequality on correlation functions for periodic signals due to Prosser. Noise signals are treated and inequalities of a similar nature are obtained for ensemble-average cross correlation functions under suitable hypotheses on the statistical properties of the noise. Inequalities of this type are the basis of a well-known method of estimating the unknown time delay of an observed signal. The extension to nondecreasing discontinuous distortion functions allows the use of hard limiting or quantization to facilitate the cross correlation calculation.     

1/f noise in n-channel silicon-gate MOS transistors

It is found that equivalent gate noise power for l/f noise in n-channel silicon-gate MOS transistors at near zero drain voltage at room temperature is empirically described by two noise terms, which vary asK_{1}(q/C_{ox}) (V_{G} -V_{T})/f and K_{2}(q/C_{ox})^{2}/f, where V_{G}is gate voltage, VTis threshold Voltage, and Coxis gate-oxide capacitance per unit area. Unification of carrier-density fluctuation (McWhorter's model)and mobility fluctuation (Hooge's model) can account for the experimental data. The comparison between the theory and experiment shows that the carrier fluctuation term K2is proportional to oxide-trap density at Fermi-level. The mobility fluctuation term K1is correlated to K2, being proportional toradic K_{2}. The origin of this correlation is yet to be clarified.     

Two-dimensional dynamic analysis of short-channel thin-film MOS transistors using a minicomputer

A computer program is described for simulating two-dimensional thin-film MOS transistors on a minicomputer. Data are presented showing the variation of internal carrier density with time until a steady-state condition is reached. These data show the formation of a drain-induced back channel whose conduction properties depend on the back-channel length and carrier mobility. For channel length below 2.0 µm, the two-dimensional steady-state drain current is shown to fit the expressionI_{D}/W = frac{micro_{0}C_{0}}{L[1+(micro_{0}/upsilon_{s} V_{D}{L})^{2}]^{1/2}}(V_{G} - V_{T} - V_{D/2})V{D}for values of drain voltage below a specific saturation value (V_{DM}); andI_{D}/W = frac{10^{-8)(V_{G} - V_{T})^{1/2}}{(T_{ox})^{1/2}L}.(V_{D} - V_{DM}) + I_{DM}for drain voltages above the saturation value.     

Some integrals involving theQ_Mfunction (Corresp.)

Some integrals are presented that can be expressed in terms of theQ_Mfunction, which is defined as begin{equation} Q_M(a,b) = int_b^{infty} dx x(x/a)^{M-1} exp (- frac{x^2 + a^2}{2}) I_{M-1}(ax), end{equation} whereI_{M-1}is the modified Bessel function of orderM-1. Some integrals of theQ_Mfunction are also evaluated.     

Calculation of Magnetic Fields due to Line Currents

A modified form of the Biot-Savart law is derived which is of particular use in the calculation and/or graphical determination of the magnetic fields due to line currents. In a linear conductor carrying a uniform current, I, the magnetic intensity at an observation point is given by begin{equation*}H = frac{2I}{R}{sin}left(frac{alpha}{2}right)end{equation*} where ? is the viewing angle to the conductor extremities and R is the effective distance measured from the observation point to the conductor along the viewing angle bisector. Examples of the application of this formula are given. These illustrate the usefulness of the formula in simplifying EMC analyses involving circuit and system emanations.     

Equipartition laws of thermal noise

Classically, the thermal noise in electricalRCcircuits andLCRseries circuits is governed by the equipartition lawfrac{1}{2}overline{CV^{2}} = frac{1}{2}kT, whereV(t)is the noise voltage developed acrossC. When quantum effects are taken into account, the equipartition law no longer holds forRCcircuits, although an equipartition law can be deemed for the measured mean square noise voltage under certain conditions. InLCRseries circuits the equipartition lawfrac{1}{2}overline{CV^{2}} = frac{1}{2}kT, changes intofrac{1}{2}overline{CV^{2}} = frac{1}{2}bar{E}(f_{0})for high-Qtuned circuits, wherebar{E}(f_{0})is the average energy of a harmonic oscillator tuned at the tuning frequency of the tuned circuit.     

Uniform linear prediction of bandlimited processes from past samples (Corresp.)

Forx(t)either a deterministic or stochastic signal band-limited to the normalized frequency intervalmidomegamid leq pi, explicit coefficients{ a_{kn} }are exhibited that have the property that begin{equation} lim_{n rightarrow infty} parallel x(t) - sum_{1}^n a_{kn} x(t - kT) parallel = 0 end{equation} in an appropriate norm and for any constant intersample spacingTsatisfying0 < T < fac{1}{2}; that is,x(t)may be approximated arbitrarily well by a linear combination of past samples taken at any constant rate that exceeds twice the associated Nyquist rate. Moreover, the approximation ofx(t)is uniform in the sense that the coefficients{ a_{kn} }do not depend on the detailed structure ofx(t)but are absolute constants for any choice ofT. The coefficients that are obtained provide a sharpening of a previous result by Wainstein and Zubakov where a rate in excess of three times the Nyquist rate was required.     

A class of composite codes (Corresp.)

Certain useful properties of the cyclic codeVare discussed with wordsV(x)=V_{1}(x)(l+x^{n})/(l+x^{n_{1}})+V_{2}(x)(l+x^{n})/(l+x^{n_{2}}), where fori=1,2,V_{i}(x)belongs to a binary codeV_{i}of lengthn_{i}.     

On theepsilon-entropy and the rate-distortion function of certain non-Gaussian processes

Letxi = {xi(t), 0 leq t leq T}be a process with covariance functionK(s,t)andE int_0^T xi^2(t) dt < infty. It is proved that for everyvarepsilon > 0thevarepsilon-entropyH_{varepsilon}(xi)satisfies begin{equation} H_{varepsilon}(xi_g) - mathcal{H}_{xi_g} (xi) leq H_{varepsilon}(xi) leq H_{varepsilon}(xi_g) end{equation} wherexi_gis a Gaussian process with the covarianeeK(s,t)andmathcal{H}_{xi_g}(xi)is the entropy of the measure induced byxi(in function space) with respect to that induced byxi_g. It is also shown that ifmathcal{H}_{xi_g}(xi) < inftythen, asvarepsilon rightarrow 0begin{equation} H_{varepsilon}(xi) = H_{varepsilon}(xi_g) - mathcal{H}_{xi_g}(xi) + o(1). end{equation} Furthermore, ff there exists a Gaussian processg = { g(t); 0 leq t leq T }such thatmathcal{H}_g(xi) < infty, then the ratio betweenH_{varepsilon}(xi)andH_{varepsilon}(g)goes to one asvarepsilongoes to zero. Similar results are given for the rate-distortion function, and some particular examples are worked out in detail. Some cases for whichmathcal_{xi_g}(xi) = inftyare discussed, and asymptotic bounds onH_{varepsilon}(xi), expressed in terms ofH_{varepsilon}(xi_g), are derived.     

Synthesis of RC Bandpass Filters

For the first time a method of designing RC bandpass filters is presented. The method consists of two steps. The first step is a scheme to locate the necessary poles and zeros that are RC realizable to produce certain bandpass characteristics. The second step is the synthesis of RC networks to produce these poles and zeros. In the first step, the conformal transformati begin{equation*}s(z) = {left(frac{sn^{2}(z,k) - sn^{2}(alpha{K,k})}{sn^{2}(alpha{K,k})[1 - k^{2}sn^{2}(alpha{K,k})sn^{2}(z,k)]}right)}^{1/2}end{equation*} is used to map the complex frequency s plane into a rectangle in the z plane such that the passband becomes one side, and a part of the negative real axis becomes the opposite side of the rectangle. In the z plane, if poles are located along certain portions of the border and zeros in the interior of the rectangle, certain passband and stopband behavior can be achieved. Among the useful characteristics obtainable by this scheme, the following are three outstanding examples: 1) characteristics that are equal-ripple in the passband and monotonic in the stopband; 2) characteristics that are equal-ripple in the passband and have a number of transmission zeros in the stopband; and 3) characteristics with a maximum gain at the band center and monotonic elsewhere. The steepness of attenuation outside the passband can be altered by a change in the numbers of zeros at the origin and infinity.     

Electrically erasable buried-gate nonvolatile read-only memory

An electrically erasable buried (floating) gate memory is described. The memory is programmed by electron injection by junction avalanche. An internal voltage multiplication scheme using varactor bootstrapping is used which makes nearly 40 V available at the memory cell for programming, yet requires input voltages no higher than 25 V. Erasure takes place by modified Poole-Frenkel conduction in a Si3N4film of 700-Å thickness which overlays the buried gate. Standard silicon gate p-MOS processing is used with only minor modifications. Memory retention is excellent and is extrapolated to many years even at 150°C. Above 298 K, the time required for the charge to decay to one-half its initial value is given bylog t_{1/2} = frac{5254}{T}-frac{771}{T}√V_{E}(s)whereT(K) is the temperature and VEis the erase voltage. The endurance of the buried-gate memory is approximately 10 K write-erase cycles and is limited by electron trapping in the insulator. A fully decoded 1024-bit memory chip was designed and fabricated.     

An upper bound to the capacity of the band-limited Gaussian autoregressive channel with noiseless feedback

Upper bounds to the capacity of band-limited Gaussianmth-order autoregressive channels with feedback and average energy constraintEare derived. These are the only known hounds on one- and two-way autoregressive channels of order greater than one. They are the tightest known for the first-order case. In this case letalpha_1be the regression coefficient,sigma^2the innovation variance,Nthe number of channel iterations per source symbol, ande = E/N; then the first-order capacityC^1is bounded by begin{equation} C^1 leq begin{cases} frac{1}{2} ln [frac{e}{sigma^2}(1+ mid alpha_1 mid ) ^ 2 +1], & frac{e}{sigma^2} leq frac{1}{1- alpha_1^2} \ frac{1}{2} ln [frac{e}{sigma^2} + frac{2mid alpha_1 mid}{sqrt{1-alpha_1^2}} sqrt{frac{e}{simga^2}} + frac{1}{1-alpha_1^2}], & text{elsewhere}.\ end{cases} end{equation} This is equal to capacity without feedback for very low and very highe/sigma^2and is less than twice this one-way capacity everywhere.     

Erase and Retention Improvements in Charge Trap Flash Through Engineered Charge Storage Layer

The simultaneous improvement in the erase and retention characteristics in a TANOS $(hbox{TaN}{-}hbox{Al}_{2}hbox{O}_{3}{-}hbox{Si}_{3}hbox{N}_{4}{-}break hbox{SiO}_{2}{-}hbox{Si})$ Flash memory transistor by utilizing the band-engineered and compositionally graded $hbox{SiN}_{x}$ trap layer is demonstrated. With the process optimizations, a $≫ hbox{4}$ V memory window and excellent 150 $^{circ}hbox{C}$ 24-h retention (0.1–0.5 V charge loss) for a programmed $Delta V_{t} = hbox{4} hbox{V}$ with respect to the initial state are obtained. The band-engineered $hbox{SiN}_{x}$ charge storage layer enables Flash scaling beyond the floating-gate technology with a promise for improved erase speed, retention, lower supply voltages, and multilevel cell applications.      

On the capacity of certain additive non-Gaussian channels

A model of an additive non-Gaussian noise channel with generalized average input energy constraint is considered. The asymptotic channel capacityC_{zeta}(S), for large signal-to-noise ratioS, is found under certain conditions on the entropyH_{ tilde{ zeta}}( zeta)of the measure induced in function space by the noise processzeta, relative to the measure induced bytilde{zeta}, where is a Gaussian process with the same covariance as that ofzeta. IfH_{ tilde{zeta}}( zeta) < inftyand the channel input signal is of dimensionM< infty, thenC_{ zeta}(S)= frac{1}{2}M ln(1 + S/M) + Q_{zeta}( M ) + {o}(1), where0 leq Q_{ zeta}( M ) leq H_{ tilde{ zeta}}( zeta). If the channel input signal is of infinite dimension andH_{ tilde{ zeta}}( zeta) rightarrow 0forS rightarrow infty, thenC_{ zeta}(S) = frac{1}{2}S+{o}(1).     

Channel waveguides in glass via silver-sodium field-assisted ion exchange

Multimode channel waveguides were formed by field-assisted diffusion of Ag+ ion from vacuum-evaporated Ag films, into a sodium aluminosilicate glass reported to yield high diffusion rates for alkali ions. Two-dimensional index profiles of channel waveguides formed by diffusion from a strip aperture were controlled by means of diffusion time, temperature, and electric field. The diffusion equation for diffusion through a strip aperture in the presence of a one-dimensional electric field was solved. Its solution was in agreement with measured concentration profiles:frac{C(x,y,t)}{C_{0}} = frac{1}{2} { erf (frac{a - x}{2sqrt{Dt}}) + erf (frac{a + x}{2sqrt{Dt}})}.frac{1}{2} { erfc (frac{y - muE_{y}t}{2sqrt{Dt}}) + e^{(yE_{y}/D)} erfc (frac{y + muE_{y}t}{2sqrt{Dt}})}Diffusion coefficients in this aluminosilicate glass were determined to beD =(2.41 times 10^{-13}) (frac{m^{2}}{s})).exp (frac{-3.1 times 10^{4}frac{J}{mol}}{RT})Diffusion coefficients were higher (between 150°C and 300°C) than those of a low-iron soda-lime silicate glass "standard" also studied, for which diffusion coefficients wereD =(3.28 times 10^{-13} (frac{m^{2}}{s})).exp (frac{-3.6 times 10^{4}}{RT} (frac{J}{mol}))This difference in diffusion coefficients is due to the higher activation energy of diffusion in the soda-lime silicate glass. The Gladstone-Dale relation was used to calculate the maximum possible refractive index change via Ag+-Na+ ion-exchange for each type of glass. The maximum index change in the sodium aluminosilicate glass is found to be about 65 percent of that in the soda-lime silicate glass.     

On mean-square aliasing error in the cardinal series expansion of random processes (Corresp.)

An upper bound is derived for the mean-square error involved when a non-band-limited, wide-sense stationary random processx(t)(possessing an integrable power spectral density) is approximated by a cardinal series expansion of the formsum^{infty}_{-infty}x(n/2W)sinc2W(t-n/2W), a sampling expansion based on the choice of some nominal bandwidthW > 0. It is proved thatlim_{N rightarrow infty} E {|x(t) - x_{N}(t)|^{2}} leq frac{2}{pi}int_{| omega | > 2 pi W}S_{x}( omega) d omega,wherex_{N}(t) = sum_{-N}^{N}x(n/2W)sinc2W(t-n/2W), andS_{x}(omega)is the power spectral density forx(t). Further, the constant2/ piis shown to be the best possible one if a bound of this type (involving the power contained in the frequency region lying outside the arbitrarily chosen band) is to hold uniformly int. Possible reductions of the multiplicative constant as a function oftare also discussed, and a formula is given for the optimal value of this constant.     

A simple analysis of the stable field profile in the supercritical TEA

An analytical investigation supported by numerical calculations has been performed of the stable field profile in a supercritical diffusion-stabilized n-GaAs transferred electron amplifier (TEA) with ohmic contacts. In the numerical analysis, the field profile is determined by solving the steady-state continuity and Poisson equations. The diffusion-induced short-circuit stability is checked by performing time-domain computer simulations under constant voltage conditions. The analytical analysis based on simplifying assumptions gives the following results in good agreement with the numerical results. 1) A minimum doping level required for stability exists, which is inversely proportional to the field-independent diffusion coefficient assumed in the simple analysis. 2) The dc current is bias independent and below the threshold value, and the current drop ratio increases slowly and almost linearly with the doping level. 3) The domain width normalized to the diode lengthLvaries almost linearly with(V_{B}/V_{T}-1)^{frac{1}{2}}/(n_{0}L)^{frac{1}{2}}where VBis the bias voltage VTis the threshold voltage, and no is the doping level. 4) The peak domain field varies almost linearly with (V_{B}/V_{T}-1)^{frac{1}{2}} (n_{0}L)^{frac{1}{2}}. Those results contribute to the understanding of the highn_{0}L-product switch and the stability of the supercritical TEA.     

Graphical Harmonic Analysis

With the Fourier transform begin{equation*}F(omega)=int^{+infty}_{-infty}f(t)text{exp}({-j}omega{t})dtend{equation*} it is not difficult to evaluate a good approximation of the envelope of F(?) simply by maximizing the integral in the second member of the preceding equation. The purpose of this document is to use the maximization technique for the graphical harmonic analysis of complex waveforms.     

4C6--Concentration and temperature dependences of spin-lattice relaxation times in ruby at helium temperatures: Relaxation in a zero magnetic field

The relaxation times T1for the grouud state levels in ruby were measured in the temperature range 4.2 to 1.6°K for the various concentrations of theCr^{3+}ionsffrom 0.05 to 0.7 percent. The dependenceT_{1}(f)of the formT_{1}^{-1}(f) = T_{1}^{-1}(0) + T_{1}^{-1}(I)f ^{n}withn simeq 2has been obtained for the different transitions. The measurements of relaxation times forpm frac{1}{2} leftrightarrow pm frac{3}{2}transition at zero magnetic field were especially aimed at establishing a form of dependenceT_{1}(f)because of the absence of the cross relaxation effects in this case. The normal temperature dependenceT_{1} propto T_{1}^{-1}has been obtained at all concentrations in comparison with anomalous dependences observed at high concentrations by some researchers.