On restoring band-limited signals

The problem of reconstruction of band-limited signals from discrete and noisy data is studied. The reconstruction schemes employing cardinal expansions are proposed and their asymptotical properties are examined. In particular, the conditions for the convergence of the mean integrated squared error are found and the rate of convergence is evaluated. The main difference between the proposed reconstruction scheme and the classical one is in treating the sampling rate and the reconstruction rate differently. This distinction is necessary to ensure consistency of the reconstruction scheme in the presence of noise     

Recovering of autoregressive spectral estimates of signals buried in noise

In this paper, we propose a noise modeling that does not destroy AR structure of buried signals in noise independently of its nature (white or colored, Gaussian or not) and its variance. Expression of perturbed AR coefficients is derived and proposed restoration does not use any a-priori information on the nature of noise and its variance. It is shown that AR coefficients are closer to nominal ones (noise-free) in the presence of noise for lower frequency contents with respect to the sampling frequency of corresponding continuous-time processes from which samples are taken for AR estimation. For unknown frequency contents, denoising of AR coefficients is obtained by decreasing the time interval separating samples used by AR estimation. A model order selection adapted to degraded signal-to-noise ratios is proposed. Performances of the proposed recovering of original AR spectra are demonstrated via signals buried in white and colored noise. Observed results are in accordance with the developed theory.     

Reconstruction of band-limited signals from local averages

The sampling theorem says that every band-limited signal is uniquely determined by its sampled values provided the sampling points satisfy certain conditions. However, sampled values obtained in practice may not be the exact values of a signal at sampling points, but only averages of the signal near these points. Grochenig (1992) proved that band-limited signals can be reconstructed exactly from local averages if the sampling density is large enough. We study the reconstruction of band-limited signals from local averages with symmetric averaging functions. We study the aliasing error arising when a non-band-limited signal is reconstructed from local averages and give explicit error bounds. Since the classical "point sampling" can be viewed as a limiting case of average sampling, we indeed give new aliasing error bounds for both regular and irregular sampling     

Digital representations of operators on band-limited random signals

Sampling representations of bounded linear operators (BLOs) acting on extended classes of band-limited signals are derived. These are classes of deterministic signals that are not necessarily square-integrable and random signals with covariance functions that are not necessarily square-integrable on the plane. These classes consist of signals whose Fourier transforms, defined as generalized functions (or distributions), have supports that are subsets of compact sets. The merit of these representations lies in the fact that the image of a signal under an operator may be reconstructed from the samples of the original signal rather than the samples of the image. For example, the derivative of a signal, of any order, may be expressed in terms of the samples of the signal itself instead of the samples of the derivative     

Sampled data reconstruction of deterministic band-limited signals (Corresp.)

In obtaining a discrete set of data points to represent a signal, the problem of how to obtain sufficient information about the signal can become pronounced if the rate of obtaining samples of the signal is limited. The multiple-channel interpolation scheme presented in this correspondence uses periodic samples of the output of a set of prefilters excited by a deterministic input signal to reconstruct the original input signal. The input signals considered are band limited, and the sampling rate proposed is less than the Nyquist rate. This procedure may have applications in the analysis of transient signals.     

New method and circuit for processing of band-limited periodic signals

The paper presents a reconstruction of analogue multi-harmonic signals, from a number of integrated values of input signals. Based on the value of the integral of the original input signal, with a known frequency spectrum but unknown amplitudes and phases, a reconstruction of its basic parameters is done by the means of derived analytical and summarized expressions. It is applied to signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. The proposed method of processing can be used for precise RMS measurements (or power and energy) of periodic signal based on the presented signal reconstruction. Subsequent calculation of all relevant indicators related to the monitoring and processing of ac voltage and current signals is provided in this manner. The paper investigates the errors related to the signal parameter estimation, and there is a computer simulation that demonstrates the accuracy of these algorithms.     

A new extrapolation algorithm for band-limited signals using theregularization method

The ill-posedness of the extrapolation problem in the presence of noise is considered. A stable algorithm is constructed by solving a Fredholm equation based on a regularization method. The algorithm appears relatively robust, since the noise η_δ(t ) is taken as a function in L²[-T,T](T>0) such that the error energy ∫|η_δ(t)|² dt⩽δ², where integration is from - T to T, and the constructed extrapolation uniformly converges to the desired signal over (-∞, +∞) as δ→0. An estimate for the error energy of the constructed extrapolation over (-∞, +∞) and for the absolute error between the constructed extrapolation and the desired signal over (-∞, +∞) are presented     

Reconstruction of nonuniformly sampled band-limited signals and jitter error reduction

The restoration of a band-limited signal from its unequally spaced samples is considered. The proposed method is based on the correction of a response of an ideal LPF to the sampling data. The ideal LPF response to the unequally spaced samples is simply divided by a distribution function specified by the sampling times of the input data. The jitter error resulting from the application of the proposed method is evaluated. It is shown that the increase in sampling time deviations from their synchronous positions increases the efficiency. The proposed method is shown to give a more accurate signal restoration than the traditional one.     

二维带限高斯噪声的FPGA实现

m序列具有良好的伪随机性,可作为随机白噪声源,经过适当的带限滤波,可以得到带限高斯噪声。首先分析了高斯白噪声的特点,然后设计了利用FPGA产生带限高斯噪声的电路,经正交调制,送DAC输出,得到了较为理想的二维带限高斯噪声,最后对产生的噪声信号进行了测试。设计中始终考虑到节省FPGA资源,同时也达到了降低功耗、节约成本的目的。     

Bounds for truncation error in sampling expansions of band-limited signals

Forf(t)a real-valued signal band-limited to- pi r leq omega leq pi r (0 < r < 1)and represented by its Fourier integral, upper bounds are established for the magnitude of the truncation error whenf(t)is approximated at a generic timetby an appropriate selection ofN_{1} + N_{2} + 1terms from its Shannon sampling series expansion, the latter expansion being associated with the full band[-pi, pi]and thus involving samples offtaken at the integer points. Results are presented for two cases: 1) the Fourier transformF(omega)is such that|F(omega)|^{2}is integrable on[-pi, pi r](finite energy case), and 2)|F(omega)|is integrable on[-pi r, pi r]. In case 1) it is shown that the truncation error magnitude is bounded above byg(r, t) cdot sqrt{E} cdot left( frac{1}{N_{1}} + frac{1}{N_{2}} right)whereEdenotes the signal energy andgis independent ofN_{1}, N_{2}and the particular band-limited signal being approximated. Correspondingly, in case 2) the error is bounded above byh(r, t) cdot M cdot left( frac{1}{N_{1}} + frac{1}{N_{2}} right)whereMis the maximum signal amplitude andhis independent ofN_{1}, N_{2}and the signal. These estimates possess the same asymptotic behavior as those exhibited earlier by Yao and Thomas [2], but are derived here using only real variable methods in conjunction with the signal representation. In case 1), the estimate obtained represents a sharpening of the Yao-Thomas bound for values ofrdose to unity.     

All-digital 2-channel parallel undersampling and reconstruction of band-limited signals

In this paper, we show that a band-limited signal can be reconstructed from two undersampled sequences of the signal, and further propose a 2-channel multirate undersampling and reconstruction method for band-limited signals. With such an approach, the sampling rate can be reduced to about one half of the Nyquist sampling rate. This method also has the advantage that no analog filters are needed to decompose the signal into two components with narrower bandwidths. Furthermore, the parallel processing of the two sampled sequences will lead to improved system performances. Finally, we consider the synchronization between the two sampled sequences, and show that the two A/D converters can be readily synchronized.     

脉冲噪声下跳频信号时频图修正

为了在α稳定分布噪声的环境下获得清晰的跳频信号时频图,提出一种基于分数低阶SPWVD(Smoothed Pseudo Wigner-Vile Distribution)与形态学滤波相结合的跳频信号时频图修正算法。首先,根据接收到的多跳频信号建立跳频信号的模型和α稳定分布噪声模型;然后,采用低阶SPWVD变换抑制时频图中脉冲噪声;最后,根据形态学滤波处理方法对残留噪声进一步抑制进而得到清晰时频图。理论分析和仿真结果表明,所提算法在广义信噪比为-5 dB时仍可以得到清晰可靠的跳频信号时频图,并且基于时频图的参数估计性能优良。     

Testing parametric assumptions on band- or time-limited signals under noise

This paper considers the problem of testing parametric assumptions on signals f from which only noisy observations y/sub k/=f(/spl tau/k)+/spl epsi//sub k/ are available, and where the signal is assumed to be either band-limited or time-limited. To this end, the signal is reconstructed by an estimator based on the Whittaker-Shannon (WS) sampling theorem with oversampling. As test statistic, the minimal L/sub 2/ distance between the estimated signal and the parametric model is used. To construct appropriate tests, the asymptotic distribution of the test statistic is derived both under the hypothesis of the validity of the parametric model and under fixed local alternatives. As a byproduct, the asymptotic distribution of the integrated square error of the estimator is computed, which is of interest by itself, e.g., for the analysis of a cross-validated bandwidth selector.     

Truncation error bounds for the cardinal sampling expansion of band-limited signals

Bounds are derived for the truncation error of the cardinal sampling expansion for a large class of band-limited deterministic and random signals. These bounds extend and improve upon the bounds available in the literature.     

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.     

On the reconstruction of band-limited multidimensional signals from algebraic sampling contours

In this letter we pose and answer the following question: Is a band-limited multidimensional signal uniquely determined by a continuous set of samples whose location is given by the zeroes of a polynomial equation? Applications to the theory of reconstruction of finite-extent objects from a set of generalized projections are discussed including the classical problems of parallel X-ray and diffraction tomography.     

Reconstruction of band-limited periodic nonuniformly sampled signals through multirate filter banks

A band-limited signal can be recovered from its periodic nonuniformly spaced samples provided the average sampling rate is at least the Nyquist rate. A multirate filter bank structure is used to both model this nonuniform sampling (through the analysis bank) and reconstruct a uniformly sampled sequence (through the synthesis bank). Several techniques for modeling the nonuniform sampling are presented for various cases of sampling. Conditions on the filter bank structure are used to accurately reconstruct uniform samples of the input signal at the Nyquist rate. Several examples and simulation results are presented, with emphasis on forms of nonuniform sampling that may be useful in mixed-signal integrated circuits.     

THE CHAOTIC DETECTION OF PERIODIC SHORT—IMPULSE SIGNALS UNDER STRONG NOISE BACKGROUND

The periodic short-impulse signals under strong noise background are successfully detected with a special chaotic system invented by the authors.Simulation experiments show that the chaotic system is very sensitive to periodic shor-impulse signals submerged by strong noise background,and it can effectively restrain any zero-mean nose.The system has a stable working-detection limit of -83dB.     

Exact solution for control loop adaptive antenna weights in band-limited noise

A technique is presented that yields exact solutions for the noise analysis of the Applebaum adaptive algorithm. Past researchers have derived results under the assumption that the input noise is rapidly varying with respect to the output weighting vector of the Applebaum algorithm. In this paper, this work has been extended to include noise that can vary at any rate. External noise sources are modeled as continuous state jump Markov processes (CSJMP) which results in exact first moment equations for the weighting vector that are solvable. Specifically, the case where the adaptive algorithm is subjected to a single external noise source is examined in detail. Results in adaptive processing convergence times and average null depth are presented.