Spectral properties of photocurrent fluctuations in avalanchephotodiodes

The authors provide a stochastic model that describes the time dynamics of double-carrier multiplication in an avalanche photodiode (APD) and obtain the autocorrelation function and the spectral characteristics of the photoelectric current. The photoelectric pulse generated by an APD as a result of a single injected photoelectron is regarded as a nonstationary random function of time (the impulse response function). A discrete stochastic model for the electron-hole motion and multiplication is defined on a spatiotemporal lattice and used to derive recursive equations for the mean, the variance, and the autocorrelation of the impulse response as functions of time. Correlation properties of the impulse response are studied for a conventional and a multilayer (superlattice) APD. The power spectral density of the photocurrent is evaluated     

A new approach for computing the bandwidth statistics of avalanchephotodiodes

A new approach for characterizing the avalanche-buildup-time-limited bandwidth of avalanche photodiodes (APD's) is introduced which relies on the direct knowledge of the statistics of the random response time. The random response time is the actual duration of the APD's finite buildup limited random impulse response function. A theory is developed characterizing the probability distribution function (PDF) of the random response time. Recurrence equations are derived and numerically solved to yield the PDF of the random response time. The PDF is then used to compute the mean and the standard deviation of the bandwidth. The dependence of the mean and the standard deviation of the bandwidth on the APD mean gain and the ionization coefficient ratio is investigated. Exact asymptotics of the tail of the PDF of the response time are also developed to aid the computation efficiency. The technique can be readily applied to multiplication models which incorporate dead space and can be extended to cases for which the carrier ionization coefficient is position dependent     

Evaluation of transient response using state variables

A certain equivalent state-variable representation of a system defined by a rational transfer function, and stimulated by an impulse function, leads to equations in which not only the impulse response but also the step response and, if need be, the ramp response, are simply derived from the state variables.     

On the distribution of zeros of mobile channels with application toGSM/EDGE

The distribution of zeros of mobile channels is investigated and the results obtained are applied to the GSM/EDGE system. The taps of the discrete-time overall impulse response can be modeled as correlated complex Gaussian random variables, where the correlations depend on the transmit filter, the power delay profile of the channel, and the receiver input filter. For calculation of the density of zeros of the overall transfer function, a result from the mathematical literature is used. From this density, two cumulative distributions which are relevant for the design of suboptimum receivers are derived. Our investigations show that for the power delay profiles specified for GSM/EDGE, an allpass prefilter which transforms the impulse response in its minimum phase equivalent should be employed if decision-feedback equalization (DFE) or reduced-state sequence estimation (RSSE) are used at the receiver. On the other hand, if impulse response truncation using a linear prefilter is applied, the truncated impulse response should have a length of three as shown     

Analytic characterization of dynamic optical switching of symmetricself-electrooptic effect devices in extremely shallow quantum wells

An analytical expression of the impulse response of extremely shallow quantum well (ESQW) p-i-n photodiodes is presented. The response function incorporates the effects of the LO phonon scattering rate in the well and the carrier transport coefficients in the continuum states. The result thus obtained has been applied to ESQW symmetric SEEDs (symmetric E-SEEDs) for analyzing the switching characteristics in time. The impulse response function is derived, and the circuit equations of symmetric SEEDs (S-SEEDs) are examined. Specifically, it is pointed out that the RC time constant inherent in S-SEEDs speeds up the down-switching (from reverse to forward), while delaying the up-switching (from forward to reverse) of the two diode voltages involved. The analytic solutions of the two diode voltages in symmetric E-SEEDs are given as a function of time during the dynamic optical switching     

Robust Transmitted Waveform and Received Filter Design for Cognitive Radar in the Presence of Signal-Dependent Interference

The problem of robust transmitted waveform and received filter design for cognitive radar in a signal-dependent interference environment is considered. When estimate errors of the target impulse response (TIR) and clutter impulse response (CIR) exist, in order to improve the worst signal-to-clutter ratio (SCR) and signal-to-interference-and-noise ratio (SINR), a robust transmitted waveform and received filter are designed based on the minimax criterion by using the information fed back from the receiver. Using deterministic and random models, the waveform and filter design problem is divided into three optimization problems. The robust waveform and filter are then obtained by solving these problems. In the deterministic model, we prove that the robust waveform and filter impulse response can be generated by a pseudorandom code. In the random model, the robust waveform and filter impulse response can be obtained by an alternative projection algorithm. Numerical results indicate that the worst SINR of the robust waveform and filter is higher than that of the traditional waveform and filter.     

Current impulse response of thin InP p-i-n diodes

The simulation of current impulse response using random response time model in avalanche photodiode (APD) is presented. A random response time model considers the randomness of times at which the primary and secondary carriers are generated in multiplication region. The dead-space effect is included in our model to demonstrate the impact on current impulse response of thin APDs. Current impulse response of homojunction InP p⁺-i-n⁺ diodes with the multiplication widths of 0.1 and 0.2 μm are calculated. Our results show that dead-space gives a slower decay rate of current impulse response in thin APD, which may degrade the bit-error-rate of the optical communication systems.     

关于电学基础课程物理量的量纲与单位的讨论

本文从“量”的等式观点出发,阐述了电学基础课程相关物理量的量纲与单位问题,包括将已知量代入方程的方法,导出量纲与导出单位,标准函数的量纲等。特别指出,单位冲激函数的量纲是倒时间量纲,单位阶跃特性s(t)与单位冲激特性h(t)都是响应与激励量值的某种比值,它们都不具有电压或电流的量纲,不是普通意义上的响应。唯此,卷积积分公式的量纲才能平衡。本文目的是激发广大教师在课程教学中努力探索量纲问题的积极性。     

Time and frequency response of the conventional avalanche photodiode

An analytical expression for the time course of the average impulse response function for a conventional avalanche photodiode is derived. Delta-function absorption of a single photocarrier and single-carrier-initiated/single-carrier multiplication conditions are assumed. The result is obtained as a limiting case of a previously derived equation for the staircase avalanche photodiode. The initial exponential growth of the curves is shown to represent electron and hole contributions arising from multiplication in the avalanche region whereas the subsequent exponential decay arises from residual holes transiting backward across the multiplication region. The associated frequency response function is obtained by Fourier transformation. The analytical results are shown to be in good accord with average impulse response functions obtained by Riad and Hayes by means of simulation from the transport equations. The results should also apply to the channeling avalanche photodiode and to related structures in which the carriers are spatially separated and the multiplication is essentially single-carrier like.     

A time domain approach for the fluctuation analysis of heart raterelated to instantaneous lung volume

A time domain technique for estimating transfer characteristics from fluctuations of instantaneous lung volume (ILV) to heart rate (HR) is presented. An effective procedure for estimating the impulse response of HR to ILV is proposed. Pre- and post-processing procedures, including prefiltering of the HR signal, preenhancement of the high frequency content of the ILV signal, and post-filtering of the estimated impulse response, together with a random breathing technique, are shown to effectively reduce spurious transfer gain so as to get a stable estimate of the impulse response. Analysis of the data collected from fourteen healthy male subjects in various conditions revealed that there are three components in the impulse response: fast positive, delayed slow negative, and oscillatory. The effects of the autonomic blocking agents propranolol and atropine on these transfer characteristics are also described     

A simple and efficient design of variable fractional delay FIR filters

In this paper, a simple and efficient approach for designing one-dimensional variable fractional delay finite impulse response digital filters is proposed. Two matrix equations, based respectively on the weighted least-squares function of the optimum fixed fractional delay filter and the filter coefficient polynomial fitting, are formulated in tandem to form the design algorithm, which only has the computation complexity comparable with that of designing fixed finite impulse response digital filters. A design example is also given to justify the effectiveness and advantages of the proposed design method.     

Blind deconvolution of symmetric noncausal impulse responses usingtwo-sided linear prediction

Considers the problem of estimating the time-symmetric, noncausal impulse response of a linear time-invariant system from measurements of the response of the system to an unknown input signal, which is assumed to be a realization of a white random process. The symmetric impulse response is modeled by a two-sided AR or ARMA system model. The two-sided AR coefficients are estimated using a two-step procedure. First, an estimate of an unconstrained parameter vector is computed by solving a close-to-Toeplitz-plus-Hankel system of equations using previously developed fast algorithms. Then, the polynomial square root of the result is obtained by solving a constrained least-squares problem which has a simple solution. Unlike previous methods, this approach requires no iterative procedure. However, it may lead to an unstable model in some extreme cases. Simulation results illustrate the performance of the proposed methods     

Optimal finite impulse response approximate inverse of linear periodic filters

A method to construct an optimal finite impulse response (FIR) approximate inverse for discrete-time causal FIR periodic filters in the presence of measurement noise is proposed. The objective function to be minimised is the sum-of-mean-square errors over one period. On the basis of the matrix impulse response of the multi-input multi-output time-invariant representation of periodic filters, the optimisation problem is formulated as one that minimises the summed equation errors of a set of over-determined linear equations. It is shown that the problem is equivalent to a set of least-squares problems from which a simple, closed-form solution is obtained. Numerical examples are used to illustrate the performance of the proposed FIR approximate inverse.     

Blind estimation of a fractionally sampled FIR channel for OFDM transmission using residue polynomials

This paper introduces blind-channel estimation methods using residue polynomials for orthogonal-frequency-division-multiplexing (OFDM) transmission under the assumption that the channel is finite-impulse response (FIR). In terms of z transform, if the received signal is multiplied by the inverse of the transmitted signal, the resulting z transform renders the channel transfer function when additive noise is absent in the channel. For an FIR channel, samples of the recovered impulse response must be zero in the region of zeros of the channel impulse response. Based on this observation, the blind estimation problem is formulated as a solution of linear equations, treating the transmitted symbols as unknown variables. Polynomial residue arithmetic turns out to be very useful for deriving the linear equations. The proposed method is computationally more efficient than subspace methods that are applied for OFDM transmission systems. In addition, unlike subspace methods, the proposed method is deterministic and does not require estimation of the autocorrelation matrix of received signals, which is required in subspace methods.     

Impulse response modeling of indoor radio propagation channels

If indoor radio propagation channels are modeled as linear filters, they can be characterized by reporting the parameters of their equivalent impulse response functions. The measurement and modeling of estimates for such functions in two different office buildings are reported. The resulting data base consists of 12000 impulse response estimates of the channel that were obtained by inverse Fourier transforming of the channel's transfer functions. It is shown that the number of multipath components in each impulse response estimate is a normally-distributed random variable with a mean value that increases with increasing antenna separations; a modified Poisson distribution shows a good fit to the arrival time of the multipath components; amplitudes are lognormally distributed over both local and global areas, with a log-mean value that decreases almost linearly with increasing excess delay; for small displacements of the receiving antenna, the amplitude of the multipath components are correlated; the amplitudes of adjacent multipath components of the same impulse response function show negligible correlations; and the RMS delay spread over large areas is normally distributed with mean values that increase with increasing antenna separation     

Characterization of the Arterial System in the Time Domain

The impulse response function and the input impedance of the systemic arterial tree emphasize different aspects of this system. The impulse response function is calculated via inverse Fourier transformation of the input impedance. The effects of truncation of the impedance are reduced by subjecting the data to a Dolph-Chebyshev filter. The impulse response functions of a windkessel model, a uniform tube model, and of the arterial system of the dog, are given. The impulse response functions of the windkessel model and of the arterial system of the control dog show a sharp initial peak followed by an exponential decay (equal decay time as that of the diastolic pressure tracing). The height of the decay extrapolated to time zero is related to total arterial compliance. Total arterial compliance calculated in this way agrees with the value calculated from the ratio of the time constant of the diastolic pressure decay and peripheral resistance. The presence of peaks in the impulse response function indicates a distinct reflection site as shown in the uniform tube model and found in the dog with balloon occlusion of the descending aorta. The measurement of the time intervals between these peaks and the start of excitation together with the pulse wave velocity enable us to calculate the distance between the location of the reflecting site and the heart.     

Transmission Distortion in Multimode Random Waveguides

We consider the coupled line equations for two-mode random media in which both modes travel in the same (forward) direction as a model for multimode millimeter waveguides and optical fibers, in which mode conversion at imperfections occurs primarily in the forward direction. Some exact general properties satisfied by the transfer function and the impulse response of such a system are given for an arbitrary coupling coefficient. A random stationary coupling coefficient with statistically independent successive values, and consequently a white spectrum (e.g., a white Gaussian or a Poisson noise), permits exact determination of transmission statistics; we obtain first- and second-order statistics in the time and frequency domains. No perturbation or other approximations are made in any of the above results, which are obtained directly from the coupled line equations. These results are used to study signal distortion in long guides. By straightforward extension of this work more complicated calculations can treat more forward modes, but not backward modes or nonwhite coupling coefficient spectra. In this paper the coupling coefficient is assumed frequency independent, and under certain conditions the signal distortion decreases as the mode conversion increases. In practical cases the coupling coefficients are frequency dependent and the above behavior is modified; the present work is extended to this important case in a companion paper.     

谐波共焦显微镜的成像原理

根据非线性光学理论,讨论了谐波成像的原理和性质.通过二次谐波(SHG)、和三次谐波(THG)的耦合方程的讨论,指出SHG、THG成像具有很好的相干性,属于相干成像.这足因为,方程里没有含随机位相的项,却含有位相随样本厚度:变化的项.利用SHG、THG共焦显微镜成像的强度脉冲响应函数,导出截止频率表达式,同时表明了谐波成像原理的优越性.     

Maximum energy signals for random time-varying channels (Corresp.)

Maximum energy transfer is usually considered a primary signal design criterion for random time-varying channels. The signal that maximizes the average energy transferred through these channels is given as the solution to a Freholm integral equation. The kernel is completely specified by the autocorrelation function of the impulse response.     

Factors Affecting the Measured Value of Impulse Bandwidth

The errors introduced in the measured value of impulse bandwidth obtained by determining the area under the response curve are discussed. The required pulse width of a narrow pulse used to stimulate the impulse response of a linear network is also analyzed. The results are presented in terms of the integral-square error between the true impulse response and simulated response as a function of band-width-pulse-width product. The trapezoidal method of numerical integration as applied to this measurement is briefly discussed.