Estimation of probability density function using spectral analysis

The authors present a new bound on the estimation of the probability density function of random signals, using Woodward's theorem, correlation techniques and spectral analysis. The proposed method is based on the spectral analysis of the random process     

一种可监测人体脉搏波及心率的健康鼠标

脉搏波的波形特征与心血管疾病密切相关,为此用户需要一种简单、实时的便携装置。通过安装在正常使用鼠标时大拇指触摸到的鼠标位置的反射式脉搏波光电传感器采集脉搏波信号,信号经过滤波、放大和A/D转换后,利用单片机对脉搏波信号处理并得出心率数据,最后通过USB接口连接电脑端软件显示。将鼠标和反射式光电传感器结合制成成品之后,经过实际测试,传感器能够很好的测得手指脉搏波并输出。这种可监测人体脉搏波及心率的健康鼠标可以在用户使用鼠标的不经意状态时检测并记录脉搏波及心率。     

A new approach to analysis of residue probability density function in pipelined ADCs

This paper presents a new approach to analysis of residue probability density function (pdf) in pipelined ADCs. This work was performed based on the fundamental theorem for function of a random variable to map stage input pdf to its output density. It will be shown that residue pdf converges to uniformity. For the stages with half-bit redundancy, this uniformity is accompanied with an extra bit of resolution. Also, the minimum number of stages required to achieve a given value of resolution improvement are studied. Investigating the impact of backend stage on this extra resolution, the appropriate backend to maintain the most extra resolution is proposed. Examining the allowable comparator offsets in different stages, we can see that with decreasing the offset errors in final stages, offset errors impact of the first stages on the final residue pdf and the total converter resolution can be eliminated.     

Asymmetric probability density function of a signal withinterferometric crosstalk

An asymmetric probability density function due to the beating of interferometric crosstalk and amplifier spontaneous emission noise in a system with optical preamplifier is observed experimentally and explained theoretically. An accurate derivation of the probability density function of the photocurrent in the presence of N incoherent homodyne interferers is presented, for the first time, to explain the asymmetry. The model is compared with the experiment and is shown to be in excellent agreement     

General probability density function of packet service times for computer networks

The letter presents derivations of a generalised probability density and distribution functions of packet service times for computer communication networks. Included in the derivation are the effects of message segmentation into packets and the effects of control traffic. We also present the first and the second moments of the packet service times. These expressions can be used in modelling and analysis of computer networks by assigning appropriate values to various parameters.     

Envelope probability density function of the sum of signal, noise and interference

A new closed-form expression of the envelope probability density function for the sum of signal, Gaussian noise and c.w. interference is found.     

Multidimensional probability density function approximations fordetection, classification, and model order selection

This paper addresses the problem of calculating the multidimensional probability density functions (PDFs) of statistics derived from known many-to-one transformations of independent random variables (RVs) with known distributions. The statistics covered in the paper include reflection coefficients, autocorrelation estimates, cepstral coefficients, and general linear functions of independent RVs. Through PDF transformation, these results Can be used for general PDF approximation, detection, classification, and model order selection. A model order selection example that shows significantly better performance than the Akaike and MDL method is included     

Estimation of probability density and distribution functions

First- and second-order stochastic gradient algorithms are developed for suitably approximating the unknown density and distribution functions of a random vector from a sequence of independent samples. The mean-square-error criterion and the integral-square-error criterion are used in the approximations. The rates of convergence and the approximation error are also evaluated.     

Generation and analysis of non-Gaussian Markov time series

Correlated non-Gaussian Markov sequences can be considered as filtered white noise (independent, identically distributed sequences of random variables), the filter being a nonlinear system in general. The authors discuss the applicability of linear models and nonlinear methods based on the diagonal series expansion of bivariate densities for analyzing this system. Non-Gaussian sequences exhibit different properties in the forward and backward directions of time. The authors explore the connection to system modeling of this temporal asymmetry and some of its consequences. As an example, they analyze a first-order linear autoregressive model with hyperbolic secant amplifier distribution at its output     

Measurement and modelling of the probability density function of amplitude scintillations on an X-band satellite down-link

The experimentally determined probabiliiy density function of the amplitude scintillations on an X-band satellite down-link is shown to depart significantly from the log-normal distribution for scintillations with amplitudes greater than ±0.15 dB, which occur on average for less than 5% of the time. This departure is explained in terms of a Gaussian process with a variable standard deviation, and the impact and use of this model is discussed.     

Relationship between slope probability density function and the physical optics integral in rough surface scattering

The integral for the average scattered power from a rough surface obtained from physical optics is shown to be proportional to the joint probability density function for the surface slopes in the high-frequency limit.     

The probability density function for the output of a correlator with band-pass input waveforms

A general expression is obtained for the characteristic function for the output of a correlator with narrow-band inputs. This general expression is applicable to cases in which the input signals are sinusoidal and have arbitrary amplitudes and phases, and in which the noise inputs are partially correlated. The probability density function for the output is obtained for three special cases, one of which corresponds to a situation that often arises in practice. This practical situation is that in which the signal inputs have the same amplitude and phase, and the noise inputs have the same rms value but are uncorrelated.     

Power spectral density of unevenly sampled data by least-squareanalysis: performance and application to heart rate signals

This work studies the frequency behavior of a least-square method to estimate the power spectral density of unevenly sampled signals. When the uneven sampling can be modeled as uniform sampling plus a stationary random deviation, this spectrum results in a periodic repetition of the original continuous time spectrum at the mean Nyquist frequency, with a low-pass effect affecting upper frequency bands that depends on the sampling dispersion. If the dispersion is small compared with the mean sampling period, the estimation at the base band is unbiased with practically no dispersion. When uneven sampling is modeled by a deterministic sinusoidal variation respect to the uniform sampling the obtained results are in agreement with those obtained for small random deviation. This approximation is usually well satisfied in signals like heart rate (HR) series. The theoretically predicted performance has been tested and corroborated with simulated and real HR signals. The Lomb method has been compared with the classical power spectral density (PSD) estimators that include resampling to get uniform sampling. The authors have found that the Lomb method avoids the major problem of classical methods: the low-pass effect of the resampling. Also only frequencies up to the mean Nyquist frequency should be considered (lower than 0.5 Hz if the HR is lower than 60 bpm). It is concluded that for PSD estimation of unevenly sampled signals the Lomb method is more suitable than fast Fourier transform or autoregressive estimate with linear or cubic interpolation. In extreme situations (low-HR or high-frequency components) the Lomb estimate still introduces high-frequency contamination that suggest further studies of superior performance interpolators. In the case of HR signals the authors have also marked the convenience of selecting a stationary heart rate period to carry out a heart rate variability analysis     

Respiration response curve analysis of heart rate variability

A noninvasive study was conducted on intact awake humans to characterize the dynamic response of the heart to the vagus during slow-, comfortable-, and fast-paced respiration (8, 12, and 18 breaths/min), under both sitting and standing conditions. The respiration response curve (RRC) of respiration-associated vagal effects on the heart was estimated, and characteristics of entrainment and frequency dependence on respiration were demonstrated. It was shown that the degree of entrainment and magnitude of phase resetting decrease with increase of pacing rate from 8 to 18 breaths/min. Further, the RRC was examined by overlapping equivalent phase shifts in different respiration cycles. This examination of the RRC can help one not only to find the common pattern underlying the RRC during different respiration cycles but also to perceive its variation related to degree of entrainment     

Flexible estimation of probability and cumulative density functions

A novel, simple and effective algorithm for the estimation of the probability density function and cumulative density function is presented. The algorithm is based on an information maximisation approach. The nonlinear function involved in the algorithm is adaptively modified during learning and is implemented by using a spline function.     

Outage probability and error rate analysis of full duplex relay in asymmetric fading channels

Full duplex (FD) technique has evolved as a viable solution to address the spectrum scarce issue. It has gained research interest for its potential to double the wireless link capacity and enhance spectral efficiency (SE). In this paper, the end-to-end performance of an amplify-and-forward full duplex relay(FDR) in asymmetric Rayleigh–Rician fading channels is explored, unlike the other works that assume symmetric fading conditions in both the links. The asymmetric or mixed fading channels properly model the realistic communication scenarios like satellite/terrestrial wireless communication systems. In this work, we consider that the source-relay link experiences Rayleigh fading and the relay-destination link experiences Rician fading. The novel exact and lower bound closed form analytical expressions for outage probability (OP) and bit error rate (BER) for the considered FD system are derived. Moreover, the effect of severity of fading and the amount of residual self-interference (RSI) on the performance of FDR are also studied. In addition, MC simulations are carried out to validate the results. It is observed that the performance metrics, OP and BER, are highly dependent on the severity of fading and the amount of RSI. Furthermore, it is found that typically at the SNR of 10 dB, an improvement of approximately 27.6% in OP is obtained. Also, our work offers appreciable SNR gain, for example, for a BER of 10⁻², an SNR improvement of around 11 dB is achieved. These findings have been compared with the mixed Rayleigh–Rician fading channel conditions considering only half duplex(HD) mode. These parameter metrics are helpful in analyzing the performance of FD in various communication scenarios such as LoS/NLoS conditions and hence pave the way for more realistic FDR.     

The probability density function for the output of an analog cross-correlator with correlated bandpass inputs

The probability density function (pdf) for the output of an analog cross-correlator with correlated bandpass inputs is derived. The pdf is derived by a "direct method" without resorting to the "characteristic function method," which usually requires contour integrations in a complex plane for inversion operations. The correlator consists of bandpass filters, a multiplier, and a zonal low-pass filter. We treat the general situation in which the two inputs are narrow-band signals of unequal power and of different phases. The bandpass input noises are assumed to be correlated and may have different powers. In the Appendix, another derivation for the pdf is given in the special case of equal power correlated noise. This derivation is based on the fact that the correlator output random variable is the difference of two independent noncentral chi-square variables of two degrees of freedom. We show that the two expressions for the pdf (one from the direct method and the other from the characteristic function method) are indeed equivalent. Finally, we discuss two major areas of application.     

Finding the approximate angular probability density function of wave arrival by using a directional antenna

The first-order approximate angular probability density function of wave arrival can be obtained by plotting the mean-square value of signal level versus the pointing angle of a mobile radio directional antenna during an entire test run. The accuracy of this first-order approximation is dependent on the beamwidth of the antenna. As the beamwidth of the antenna becomes narrower, the approximate density function becomes more accurate. There are also higher order approximations for obtaining a more accurate angular probability density function without narrowing the directional antenna beamwidth. These higher order approximations are related to the moments of the signal strength received by the same directional antenna used in obtaining the first-order approximation. All of these are theoretical predictions. An experimental verification using a first-order approximate angular probability density function in finding theoretical level crossing rates of a mobile radio signal is given. The theoretical level crossing rates are in fairly good agreement with the experimental ones as long as the angular probability density function is not far from a uniform distribution.     

The estimation of a probability density function from measurements corrupted by Poisson noise (Corresp.)

The estimation of a probability density function from measurements corrupted by independent additive Poisson noise is considered. An estimate is derived that is asymptotically unbiased and consistent in the quadratic mean. Also, a practical realization of the estimator is given.