Approximate reconstruction of randomly sampled signals

We study the use of polynomial interpolation to approximate a function specified by samples taken at random moments satisfying a Poisson distribution with uniform mean sampling rate. Two different selection schemes are considered to determine which samples should be used in the construction of the polynomials, and detailed error estimates are derived for each case. The results are compared with the classical interpolation methods of convolution with a smoothing window. It is concluded that only low order polynomials are useful for interpolation in the presence of noise, but that they are comparable or superior to nonadaptive convolution in most cases, as well as computationally more efficient. Some simulation experiments are presented to support the theoretical estimates.     

A consistent nonparametric spectral estimator for randomly sampled signals

In this paper, the nonparametric spectral analysis of a randomly sampled signal is discussed. For this purpose, the general form of Masry's recursive spectral estimators is considered and improved. The corresponding algorithms require the knowledge of the sampling times, the samples, and the sampling law and that the high-frequency decay of the spectrum be at least roughly known. The minimization of the asymptotic equivalent of the mean square estimation error leads to an estimator that is not only consistent but also asymptotically optimal. Theoretical and simulation results regarding this new estimator are given and compared with the standard methods. Besides, the developed theoretical framework strictly includes the case where the sampling time process is Poisson and the signal is Gaussian.     

The processing of hexagonally sampled two-dimensional signals

Two-dimensional signals are normally processed as rectangularly sampled arrays; i.e., they are periodically sampled in each of two orthogonal independent variables. Another form of periodic sampling, hexagonal sampling, offers substantial savings in machine storage and arithmetic computations for many signal processing operations. In this paper, methods for the processing of two-dimensional signals which have been sampled as two-dimensional hexagonal arrays are presented. Included are methods for signal representation, linear system implementation, frequency response calculation, DFT calculation, filter design, and filter implementation. These algorithms bear strong resemblances to the corresponding results for rectangular arrays; however, there are also many important differences. Some comparisons between the two methods for representing planar data will also be presented.     

Spectral analysis of randomly sampled signals: suppression of aliasing and sampler jitter

Nonuniform sampling can facilitate digital alias-free signal processing (DASP), i.e., digital signal processing that is not affected by aliasing. This paper presents two DASP approaches for spectrum estimation of continuous-time signals. The proposed algorithms, named the weighted sample (WS) and weighted probability (WP) density functions, respectively, utilize random sampling to suppress aliasing. Both methods produce unbiased estimators of the signal spectrum. To achieve this effect, the computational procedure for each method has been suitably matched with the probability density function characterising the pseudorandom generators of the sampling instants. Both proposed methods are analyzed, and the qualities of the estimators they produce have been compared with each other. Although none of the proposed spectrum estimators is universally better than the other one, it has been shown that in practical cases, the WP estimator produces generally smaller errors than those obtained from WS estimation. A practical limitation of the approaches caused by the sampling-instant jitter is also studied. It has been proven that in the presence of jitter, the theoretically infinite bandwidths of WS and WP signal analyses are limited. The maximum frequency up to which these analyses can be performed is inversely proportional to the size of the jitter.     

A novel algorithm for computing autocorrelation of randomly sampled sequences

Random sampling is one of the methods used to achieve sub-Nyquist sampling. This paper proposes a novel algorithm to evaluate the circular autocorrelation of a randomly sampled sequence, from which its power density spectrum can be obtained. With uniform sampling, the size of each lag (the step size) for computing an autocorrelation of a sequence is the same as the sampling period. When random sampling is adopted, the step size should be chosen such that the highest-frequency component of interest contained in a sequence can be accommodated. To find overlaps between a time sequence and its shifted version, an appropriate window is opened in one of the time sequences. To speed up the process, a marker is set to limit the range of searching for overlaps. The proposed method of estimating the power spectrum via autocorrelation is comparable in terms of accuracy and signal-to-noise ratio (SNR) to the conventional point rule. The techniques introduced can also apply to other operations for randomly sampled sequences.     

一种加窗插值FFT谐波分析方法

由于很难实现同步采样和整周期截断,因此,利用FFT算法分析电网谐波信号时存在频谱泄露和栅栏效应,影响算法的分析精度。加窗插值FFT是抑制频谱泄露和消除栅栏效应的有效方法,在此提出一种基于3项3阶Nuttall窗插值FFT的谐波分析方法,推导了插值系数公式以及各次谐波的频率、幅值和相位的修正公式。对该算法与Hanning窗、Blackman窗插值FFT算法进行Matlab仿真对比研究,验证了该算法具有更高的分析精度。     

A new approach for estimating spectra from randomly sampled sequences

Random sampling is one of the methods that can overcome the Nyquist limit when evaluating a frequency spectrum of a signal. However, the computational complexity becomesN ² as the FFT cannot be used. A new approach, called hybrid additive random sampling, is proposed. This new scheme is devised by concatenating random sampling sequences in such a way that symmetry is created in the transform kernel for reducing the computational effort while the anti-alias property is maintained. A savings of the least 75% in computation is achieved. The sampling scheme is also found to be suitable for parallel implementation. In this paper, the algorithms for generating the sampling sequence and evaluating the spectrum are described in detail. The performances of the scheme in terms of noise, accuracy, etc., are compared with genuine random sampling and another approach proposed previously. The advantages and limitations are included.     

Efficient demodulator for bandpass sampled AM signals

A simple nonlinear (quadratic) filter is shown to demodulate bandpass sampled AM signals efficiently. The filter is based upon a discrete version of the recently introduced Teager-Kaiser energy operator, but also closely resembles a complex digital sampling demodulator. Such a filter can also be implemented in analogue circuitry     

Upper bounds for the variation of sampled signals

Upper bounds for the increment of a bandlimited signal in a sampling interval are deduced by increasing integral expressions of the increment. The bounds are then expressed as simple functions of some parameters of the spectrum (bandwidth, maximum energy, moments).     

Power spectrum of sampled signals distorted by jitter

A new approach has been used to obtain general expressions for the power spectrum of sampled signals distorted by jitter and noise resulting from jitter. A time-variant delay network is used as a model of jitter sources.     

Optimal multiplexing of sampled signals on noisy channels

This paper deals with the joint optimization of transmitting and receiving filters in multiplex transmission of pulse-amplitude-modulated (PAM) signals. A mean-square-error criterion is used. The signal processes are assumed to be mutually uncorrelated and with equal power spectral densities. Transfer matrix functions for the transmitting and for the receiving filters are used as an expedient tool. It is shown that optimal multiplexing systems can be achieved with a bandwidth ofM/T. The transfer matrix functions of optimal transmitters (and corresponding optimal receivers) are defined up to premultiplication by an arbitrary unitary matrix function. This provides for freedom of choice between various multiplexing techniques like frequency-domain multiplexing, time-domain multiplexing, or combinations thereof.     

Restrictions on the effective bandwidth of sampled signals

The effective bandwidth of a sampled signal is defined. Restrictions on this effective bandwidth are obtained. The relation between the sampling rate and the error in the reconstructed time-domain signal is bounded.     

A novel frequency estimator for sampled Doppler signals

In multigate pulsed Doppler systems with serial processing the Doppler signals are retained in their sampled form. The time-discrete nature of the Doppler signals affects the procedure to estimate the average frequency of the Doppler signal. Based on computer simulation studies it is demonstrated that a time-discrete frequency estimator based on either the density of zero-crossings or the time average of the instantaneous frequency exhibit a large relative error under poor signal-to-noise conditions or in the case of relatively wide band signals. Especially, the frequency estimator based on the instantaneous frequency functions poorly for average Doppler frequencies close to the Nyquist frequency. However, restricting the detected instantaneous frequency to a specific interval around its average improves the estimator performance considerably, while it allows tracking of center frequencies beyond the Nyquist frequency. A hardware realization of this modified estimator as incorporated in a high-resolution multigate pulsed Doppler system is described. In vitro and in vivo registrations as assessed with this system demonstrate the ability of the system to track frequencies close to and beyond the Nyquist frequency.     

On the peak factors of sampled and continuous signals

Motivated by a recent letter on an infinite difference between the peak-to-average power ratios (PAPRs) of samples (a series) and a band-limited function constructed from that series, we investigate the amplitude and variations of a band-limited function and present some relevant bounds. Related aspects on sampling theorems and sampling series are also discussed     

数控机床谐波检测FFT改进算法的研究

针对数控机床在工作过程中控制系统产生谐波的现象,提出了一种加窗双峰谱线插值FFT高精度谐波检测算法。仿真实验结果表明该算法能够有效地减少栅栏效应和频谱泄露引起的误差,应用该算法能够进一步提高谐波测量仪的技术性能,为机床的改进和电网的管理提供可靠参数。     

On optimum aperture usage for randomly propagated signals

We consider a random communication channel that models, among other things, optical communication through turbulent atmosphere. We estimate signal amplitude with large apertures and show that as large an aperture as possible is best and that there exists a practically best finite transmitted amplitude.     

Comments on the peak factor of sampled and continuous signals

Peak factors of the continuous signal and a corresponding sampled sequence are considered. It is shown, by means of an illustrative example, that in spite of the fact that the peak factor of the sampled signal is bounded, the peak factor of the continuous signal may be arbitrarily large     

基于加窗插值FFT的电网谐波检测系统的研究

随着科学技术和国民经济的快速发展,电能的需求量也极大增长,同时电能质量越来越显示其重要性,电力部门和用户对电能质量的关注也日益增加。大量电力电子装置的迅速普及使得电网的谐波污染日益严重,谐波影响电力设备的安全使用,也对周围的通信系统和电网以外的设备带来危害。基于保护电力设备及合理利用电力资源的目的,采用DSP和单片机双CPU的结构,进行FFT变换、加窗插值等数字信号处理的方法,对电力参数进行准确、实时地检测。通过实验,得到了谐波次数及与之对应的有效值、谐波幅值及畸变率。