Recovery of Bandlimited Signals from Unequally Spaced Samples

A method of recovering bandlimited signals from unequally spaced samples is described. The method uses an iterative procedure which requires low pass filtering of the unequally spaced sample pulses. This is followed by resampling at the same unequally spaced times and again low pass filtering to obtain a correction signal. Repeated application of this process is shown to converge to the original signal. These results are obtained by slight modifications of the analysis in Reference 2.     

玫瑰扫描亚成像系统中非均匀采样参数的确定

在实时图像处理系统中，图像的分辨率和系统的计算量之间总存在矛盾。高分辨率意味着大数据量和较大的计算量，但较低的分辨率又会影响图像处理的质量。为了解决图像数据量和分辨率之间的矛盾。根据玫瑰扫描视场中心区域扫描频率高，扫描迹线密；边缘区域扫描频率低；扫描迹线疏的特点，提出了在玫瑰扫描红外亚成像系统中应用高斯型非均匀采样函数进行非均匀采样的新方法。讨论了图像数据量和分辨率与非均匀采样参数之间的关系，在此基础上给出了确定非均匀采样参数的方法。     

Nonuniform sampling of bandlimited modulated signals

In this paper it is shown that an unequally spaced sampling can be implemented on the base of sinc-composition function usually used in the uniform sampling expansion. The nonuniform sampler is based on a level crossing detector (LCD) which produces a sample of carrier whenever the integral of modulating function crosses a threshold level. The information about the modulated signal is contained in the carrier samples taken at the instants which are defined by modulating function. The Riemann-Stieltjes uniform integral sum representation of the Fourier transform of signal is used as a mathematical base for the derivation of the principal results. In the particular case of the representation of single-valued real positive function, the suggested method leads to the signal representation by the equally weighted sampling at the nonuniformly distributed instants. The error estimation and numerical example illustrating the methods are given.     

Extended Method of Fast Allocation of USC’s for Millimeter-Wave DWDM-ROF Transmission Over ZDSF

Four-wave mixing (FWM) may happen efficiently and introduce crosstalk at the signal channels in dense-wavelength-division- multiplexing (DWDM) systems employing zero-dispersion-shifted fiber (ZDSF). This paper presents extended method of fast allocation of unequally spaced channels (USC’s) to minimize FWM crosstalk in millimeter-wave (MMW) DWDM radio-over-fiber (ROF) systems. When all of the MMW sub-carriers are at same frequency, by spacing the channels unequally using the extended method, all FWM products except the ones bound to be generated at the signal frequencies, can be excluded from the signal channels. While when the MMW sub-carriers are allowed to be different in frequencies, all of the FWM products can be excluded from the signal channels by spacing the channels unequally. Transmission of 622 Mbit/s BPSK data over 40 kilometers ZDSF, with and without wavelength interleaving, are simulated, for both schemes with equally and unequally spaced channels. Results comparison shows that the link performances can be clearly improved, when the channels are unequally spaced using the extended method.     

On an iterative technique for recovery of bandlimited signals

It is shown that Papoulis' iteration for extrapolation of bandlimited signals belongs to a general class based on contraction mapping, with the iteration constant taken as one. This value may also be used when applying the iteration to FM demodulation or reconstruction of a signal from unequally spaced samples.     

Regularized signal reconstruction for level-crossing sampling using Slepian functions

In this paper, we propose a method for efficient signal reconstruction from non-uniformly spaced samples collected using level-crossing sampling. Level-crossing (LC) sampling captures samples whenever the signal crosses predetermined quantization levels. Thus the LC sampling is a signal-dependent, non-uniform sampling method. Without restriction on the distribution of the sampling times, the signal reconstruction from non-uniform samples becomes ill-posed. Finite-support and nearly band-limited signals are well approximated in a low-dimensional subspace with prolate spheroidal wave functions (PSWF) also known as Slepian functions. These functions have finite support in time and maximum energy concentration within a given bandwidth and as such are very appropriate to obtain a projection of those signals. However, depending on the LC quantization levels, whenever the LC samples are highly non-uniformly spaced obtaining the projection coefficients requires a Tikhonov regularized Slepian reconstruction. The performance of the proposed method is illustrated using smooth, bursty and chirp signals. Our reconstruction results compare favorably with reconstruction from LC-sampled signals using compressive sampling techniques.     

基于改进GA-FFT综合含互耦效应的不等间隔阵列赋形方向图

该文提出了一种虚拟的最小均方有源单元方向图展开方法,将不等间隔阵列的有源方向图展开为一个虚拟的均匀间隔阵列的若干单元辐射的叠加。通过该方法,对包含阵元耦合效应的不等间隔阵列方向图,可以使用快速傅里叶变换进行加速计算。并且,该文将这个方法与遗传算法(GA)相结合,得到一种改进的GA-FFT方法,可以应用于解决含阵元互耦的不均匀间隔阵列的赋形波束综合问题。最后,分别对不等间隔的偶极子阵列平顶方向图及微带阵列的余割平方方向图进行了综合,结果表明所提方法的有效性和优势。     

Effects of Frequency Allocations and Zero-Dispersion Frequencies on FDM Lightwave Transmission Systems

In long-haul frequency-division-multiplexing lightwave transmission systems, transmission characteristics are degraded by four-wave mixing (FWM) generated in optical fibers. To overcome this problem, modified repeated unequally spaced (RUS) allocations such as equally spaced RUS (ERUS) and unequally spaced RUS (URUS) allocations have already been examined. In addition, it has been shown that FWM noises decrease by separating signal frequencies and a zero-dispersion frequency in equally spaced (ES) allocations. In this paper, ES, ERUS, and URUS allocations are studied from the viewpoint of the position of the zero-dispersion frequency relative to the signal frequencies. It is revealed that FWM noises are reduced in ES, ERUS, and URUS, with an increase in the separation between the signal frequencies and the zero-dispersion frequency, and FWM noises in ERUS and URUS are much lower than FWM noises in ES.     

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     

Generation of serial CPMFSK signal

A "serial" or "one channel" approach to the design of an M-ary CPFSK (CPMFSK) generator of arbitrary modulation index has been described. Uniformly spaced quadrant samples of the signaling sinusoids are stored in a ROM, appropriately retrieved by means of a simple digital processor and finally passed through a digital-to-analog converter (DAC) followed by a discretely tracking low-pass filter (LPF) to generate the CPMFSK signal. The design and implementation procedure of the proposed generator has been presented.     

Synthesis of uniform amplitude unequally spaced antenna arrays using the differential evolution algorithm

A computationally efficient global optimization method, the differential evolution algorithm (DEA), is proposed for the synthesis of uniform amplitude arrays of two classes, i.e., unequally spaced arrays with equal phases and unequal phases. Phase-only synthesis and the synthesis of uniformly exited unequally spaced arrays (position only synthesis) are compared and it is seen that, by using the unequal spacing, the number of array elements can be significantly reduced for attaining reduced sidelobe levels. From the DEA-based synthesis of unequally spaced arrays with uniform amplitudes and unequal phases, it is found that a tradeoff exists between the size of the unequally spaced arrays and the range of phases for the same radiation characteristics. The proposed synthesis technique using uniform amplitudes, unequal spacing, and unequal phases (position-phase synthesis) not only decreases the size of the array for the same sidelobe level compared to both the phase-only synthesis and position-only synthesis but also retains their advantages.     

On Parameter Estimates of the Lossy Wave Equation

The Cramer-Rao bound (CRB) and maximum-likelihood estimates in Gaussian noise for the parameters of a sampled signal that satisfies the lossy wave equation (such as the voltage sampled along a transmission line) are derived. Results for both equally and unequally spaced samples are given. It is shown that for certain values of the wave number (frequency) the estimates are sensitive to the amount of the ldquoreflected waverdquo in the signal, while for other values of the wave number the estimates are insensitive. It is also shown that for certain special cases it is possible to improve on standard frequency estimation (up to 3.6 dB) by reflecting some of the (noise-free) signal energy into a backward-propagating wave and applying the maximum-likelihood estimator (MLE) to the new measured signal.     

Sampling and prefiltering effects on blind equalizer design

In the development of equalization algorithms for unknown channels, the effects of the sampling rate and the analog receive prefilter prior to discretization of the received signal are often overlooked. In this paper, these effects are investigated. The relationship between the fractionally spaced output samples of a noise-limiting prefilter and the symbol spaced output samples of a matched filter is studied for both the time-invariant and the time-varying channels. It is shown that the prefilter and the sampling rate can have significant effects on blind equalization algorithms. Thus, this paper provides a common framework for comparing different blind algorithms that are studied in the literature with different sampling rates. A case study of the well-known subspace method for blind channel identification is presented. The effects of the noise color due to the prefilter on equalizers is investigated, and the sensitivity of the truncation of the overall channel impulse response in terms of the mean squared error (MSE) performance criterion is investigated through numerical examples     

Reconstruction method for jitter tolerant data acquisition system

A waveform digitizing system tolerant to deterministic jitter can be obtained by isolating the deterministic part of the jitter and calibrating the system to eliminate its effects. Calibration of the system can be made from measured nonuniform sampling times. It will be shown that this information allows reconstructing the signal at uniformly spaced sampling times. To reconstruct a signal from its nonuniform samples, we use the Shannon expansion combined with a time stretching/compressing method. Moreover, the reconstruction of a signal from a finite number of samples introduces a truncation error. We propose, using a windowing technique, to reduce the truncation error, which improves considerably the resolution, or the number of effective bits of an analog to digital conversion system.     

Analysis of repeated unequally spaced channels for FDM lightwavesystems

In long-haul optical frequency-division-multiplexing (FDM) systems, transmission characteristics are degraded by four-wave mixing (FWM). To overcome this problem, repeated unequally spaced (RUS) channels have been recently proposed as a new frequency allocation. In this paper, frequency distribution and intensity of generated FWM lights, and a total bandwidth of signal lights of RUS channels are compared with those of already known equally spaced (ES) and unequally spaced (US) channels. It is found that intensities of generated FWM lights of RUS are less than those of ES when the number of channels and a total bandwidth of signals are common in both channels. It is also revealed that RUS has a narrower total bandwidth than US when the number of channels and the minimum channel spacing are common in both channels. Since RUS simultaneously satisfies a low FWM light intensity and a narrow signal bandwidth, it is considered that RUS is suitable for FDM lightwave transmission systems     

Reconstruction of Two-Periodic Nonuniformly Sampled Band-Limited Signals Using a Discrete-Time Differentiator and a Time-Varying Multiplier

This brief considers the problem of reconstructing a band-limited signal from its two-periodic nonuniformly spaced samples. We propose a novel reconstruction system where a finite-impulse response filter designed as differentiator followed by a time-varying multiplier recovers the uniformly spaced from the nonuniformly spaced samples. The system roughly doubles the signal-to-noise ratio with relatively few filter coefficients. The main advantage is that once the differentiator has been designed, it can be implemented with fixed multipliers, and only the coefficients of the time-varying multiplier have to be adapted when the sampling pattern changes; this reduces implementation costs substantially. In addition, the system allows an efficient polyphase implementation.     

An algebraic approach to the unequal-spaced channel-allocationproblem in WDM lightwave systems

To reduce four-wave-mixing crosstalk in high-capacity, long-haul, repeaterless, wavelength-division multiplexing (WDM) lightwave systems, the use of unequally spaced channels has been proposed. Instead of being solved by integer linear programming, the unequal-spaced channel-allocation problem is treated by constructing suitable optical orthogonal codes in optical code-division multiple-access (CDMA). An “algebraic” framework and three algorithms on finding the frequency locations of unequally spaced WDM channels are introduced, where the constructions are based on generating optical CDMA codewords with a predetermined pulse separation and “aperiodic” autocorrelation sidelobes no greater than one. The algorithms potentially provide a fast and simple alternative to solve the problem, besides the proposed computer-search method     

宽带信号的中频正交采样

在回顾并对比低通滤波法、插值法和多相滤波法三种中频正交采样方法的基础上,研究它们在宽带信号情况下的适用性,讨论宽带信号的中频正交采样方法及其工程实现,并进行计算机仿真。结果表明,低通滤波法更适合于宽带信号的中频正交化处理。     

基于压缩感知的天线远场快速测量技术

提出一种应用于天线远场测量系统的压缩感知方法,通过使用正交模拟信息转换(QAIC)结构,可以减少对数据样本的采集,缩短测量时间,并提高天线远场测试效率。为验证系统的准确性,在微波暗室中,测量标准角锥喇叭天线的远场方向图,控制正交模拟信息转换结构的测量数据采样量,低速均匀采样,获取到信号的观测数据,并采用优化算法重构恢复信号。实验表明,该系统在满足一定测量误差的条件下,减少70% 的数据采集量仍能保证测量结果的准确性,较传统暗室测试更高效。     

Timing Recovery in Digital Synchronous Data Receivers

A new class of fast-converging timing recovery methods for synchronous digital data receivers is investigated. Starting with a worst-case timing offset, convergence with random binary data will typically occur within 10-20 symbols. The input signal is sampled at the baud rate; these samples are then processed to derive a suitable control signal to adjust the timing phase. A general method is outlined to obtain near-minimum-variance estimates of the timing offset with respect to a given steady-state sampling criterion. Although we make certain independence assumptions between successive samples and postulate ideal decisions to obtain convenient analytical results, our simulations with a decision-directed reference and baud-to-baud adjustments yield very similar results. Convergence is exponential, and for small loop gains the residual jitter is proportional and convergence time is inversely proportional to the loop gain. The proposed algorithms are simple and economic to implement. They apply to binary or multilevel PAM signals as well as to partial response signals.