On the prediction of a band-limited signal from past samples

An alternate proof is given of a recent result due to A. Papoulis on predicting the current value of a wide-sense stationary band-limited random process in terms of its past samples. The possibility of such prediction is shown to be equivalent to the completeness of a certain set of complex exponentials on an interval, a property that also allows extension to the prediction of deterministic band-limited signals.     

Robust prediction of band-limited signals from past samples (Corresp.)

For a complex-valued deterministic signal of finite energy band-limited to the normalized frequency band|w| leq piexplicit coefficients{a_{kn}}are found such that for anyTsatisfying0 < T leq 1/2,left| f(t)-sum^{2n}_{k=1}a_{kn}f(t - kT)right| leq E_{f}cdot beta^{n}whereE_{f}is the signal energy andbeta doteq 0.6863. Thus the estimate off(t)in terms of2npast samples taken at a rate equal to or in excess of twice the Nyquist rate converges uniformly at a geometric rate tof(t)on(- infty , infty). The suboptimal coefficients{a_{kn}}have the desirable property of being pure numbers independent of both the particular band-limited signal and of the selected sampling rate1/T. It is also shown that these same coefficients can be used to estimate the value ofx(t)of a wide-sense stationary random process in terms of past samples.     

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 note on filter application in averaging of samples

In this contribution, the capability of filters to suppress random parts of a signal is treated in terms of their impulse and step responses. The idea is based on weighted averaging of digital data, and makes use of statistical moments of the random part of the signal and corresponding entropical uncertainty. This is illustrated by considering a low-pass FIR filter as an example. As a result, a simple recommendation is given for completing the computer-aided filter design which may be significant in measurements or communication.     

A note on antennas: Definitions and methods

Definitions of scattered and diffracted fields, originally given by R. F. Millar, are reviewed and supplemented. The definitions are used to discuss relations between results obtained by commonly used pattern prediction methods for reflector antennas.     

Generalised filters and optimum sampling frequencies for the reconstruction of bandlimited signals from past samples

Generalised first- and second-order filters are presented for the reconstruction of bandlimited signals. In each case the minimum sampling frequency is derived and the corresponding filter coefficients obtained. A tradeoff exists between the rate of convergence of the reconstruction and the sampling frequency.<>     

A note on the prediction error for small time lags into the future (Corresp.)

Explicit expressions are derived for derivatives at zero lag of the mean-square prediction error for a class of random processes that includes those with rational power spectra. A simple random process not in the class is demonstrated. A sufficient condition for membership in the class is given.     

A review of reliability prediction methods for electronic devices

A wide range of reliability prediction methods is available today for electronic systems. This article classifies the commonly used and referred to reliability prediction methodologies into some categories easy to understand. A set of selected methods, which are of relevance to many industries, the aerospace industry among others, are reviewed and the possibility they offer to address the stated objectives is assessed. Their respective advantages and shortcomings are the basis for the recommendation we make to use the methods in a combined fashion (simultaneously or successively) along the product development process.     

A note on the equivalence between strict optical orthogonal codes and difference triangle sets

Zhang (see IEEE Trans. Commun., vol.47, p.967-973, July 1999) proposed a special family of optical address codes, called strict optical orthogonal codes (S-OOCs), was proposed for fiber-optic code-division multiple-access (FO-CDMA) networks. Such codes can strictly guarantee both cross-correlation and autocorrelation functions constrained to have the value one in fully asynchronous data communications and ultra fast switching. In Zhang's work the theory and designs of S-OOC, plus several examples, comparison tables, and performance analyses were presented. In this article, we set up the equivalence between S-OOC and so-called difference triangle sets (DTS), which have been extensively studied previously. Thus, all the known constructions, bounds, and analyses for DTS can be directly applied to S-OOC.     

Efficient randomized Web-cache replacement schemes using samples from past eviction times

The problem of document replacement in Web caches has received much attention and it has been shown that the eviction rule "replace the least recently used document" performs poorly in Web caches. Instead, it has been shown that using a combination of several criteria, such as the recentness and frequency of use, the size and the cost of fetching a document, leads to a sizable improvement in hit rate and latency reduction. However, in order to implement these novel schemes, one needs to maintain complicated data structures. We propose randomized algorithms for approximating any existing Web-cache replacement scheme and thereby avoid the need for any data structures. At document-replacement times, the randomized algorithm samples N documents from the cache and replaces the least useful document from the sample, where usefulness is determined according to the criteria mentioned above. The next M相似文献   

Linear prediction from samples of a function and its derivatives

Some formulas for the prediction of the values of a band-limited function based on its samples from the past are generalized by including past samples of its first derivative. The new sums, developed by an approach based on Newton series, make it possible to double the distance between the sample points. The resulting formulas are shown to apply to the prediction problem for a large class of entire functions of exponential type. In addition, a related prediction formula which uses past samples of successively higher derivatives is shown to behave similarly to the Taylor series approximation, again for a class of functions that includes the band-limited functions.     

Recovery of signals from nonuniform samples using iterative methods

An iterative method to recover a bandlimited signal from its ideal nonuniform samples is proposed. The convergence of iterations is proved, and general regions for convergence are found. It is shown that the iterative method is also applicable to other forms of nonuniform sampling, i.e. natural sampling and interpolated sampling (such as sample-and-hold signal). Simulation results show that this method works effectively and fairly fast, and the errors after a few iterations are negligible if a particular sufficient condition is satisfied or the sampling rate is higher than the Nyquist rate     

Finite difference methods for the analysis of integrated optical waveguides

A finite difference method based on a Crank-Nicolson discretisation procedure has been implemented and applied to the analysis of propagation of optical beams in dielectric waveguides. It is based on a new formula which takes into account the correct boundary conditions. Comparisons with the well known BPM technique show a definite improvement in computer time saving, accuracy and ease of use.<>     

A systematic comparison of rain attenuation prediction methods for terrestrial paths

The available rain attenuation prediction methods have been tested and compared, and the sensitivity to various input parameters regarding both the rain structure and the rainfall intensity measuring and processing techniques has been examined, on the basis of rain data collected in the northern and central parts of Italy. Starting from the same data, some considerations about the relationship between worst month/yearly cumulative rain attenuation distributions, and the diurnal influence on them are also given.     

A comparison of prediction methods for 800 MHz mobile radio propagation

The design and installation of a mobile radio system involves the evaluation or prediction of the propagation characteristics associated with the geographical area of interest. A wide variety of prediction techniques has been developed for different mobile environments, so that the task of selecting an appropriate propagation prediction method can be difficult and complex. This is especially true for systems operating in the upper-UHF band of 800-950 MHz, where mobile radio services are rapidly growing. A practical comparison is given of current prediction techniques available in the literature (for slow lognormal fading rather than multipath Rayleigh fading), with an emphasis on three essential criteria to consider in the selection process: the type of terrain or geography covered by each method, the form of prediction provided (e.g., transmission loss estimates, field strength contour maps, etc.), and the implementation difficulty and degree of sophistication.     

A note on the scattering from a slightly rough surface

A Fourier transform approach is used to derive the bistatic radar scattering cross section of a slightly rough perfectly conducting infinite surface. A perturbation expansion is used to apply the boundary conditions, and the scattered fields are asympotically evaluated by means of the method of stationary phase. The resultant expression for the radar cross sectionsigma^{0}is shown to agree with that obtained using the method as outlined by Rice.