Reconstruction of nonuniformly sampled time-limited signals using prolate spheroidal wave functions

Shannon's sampling theory is based on the reconstruction of bandlimited signals which requires infinite number of uniform time samples. Indeed, one can only have finite number of samples for numerical implementation. In this paper, as a dual of the bandlimited reconstruction, a solution for time-limited signal reconstruction from nonuniform samples is proposed. The system model we present is based on the idea that time-limited signals which are also nearly bandlimited can be well approximated by a low-dimensional subspace. This can be done by using prolate spheroidal wave functions as the basis. The order of the projection on this basis is obtained by means of the time–frequency dimension of the signal, especially in the case of non-stationary signals. The reconstruction requires the estimation of the nonuniform sampling times by means of an annihilating filter. We obtain the reconstruction parameters by solving a linear system of equations and show that our finite-dimensional model is not ill-conditioned. The practical aspects of our method including the dimensionality reduction are demonstrated by processing synthetic as well as real signals.     

自适应小波的构造及其在信号处理中的应用

基于带限正交小波基的特性,本文采用匹配方法构造了一种新的带限尺度函数,它与信号的主要能量所在频带具有相似的特征.匹配尺度滤波器是优化滤波器,它锁定能量聚集的频带,使得所需频率分量的输出增大.原始信号能够用优化的小波实时处理.通过对脑电图信号的处理,证明本文算法是有效的.     

A new implementation for DFT based on delta modulation

This paper proposes a new implementation for DFT based on delta modulation which is different from the conventional PCM implementation. The hardware structure of the method is multiplier-free, simple and low in cost. Theoretical analyses show that its SNR can approach conventional one's, for instance, FFT. Computer simulations demonstrate that for deterministic signals, the results agree with theoretical analyses. For bandlimited Gaussian signals, we can still get results similar to the conventional DFT's if selecting the step size suitably. A hardware structure which simply consists of ROM, an adder and other auxiliary circuits is also given. This Project is supported by the National Natural Science Fundation of China.     

Blind compensation of nonlinear distortion for bandlimited signals

Nonlinear distortion of bandlimited signals results in spectral spreading. This paper develops a blind nonlinear compensation method for bandlimited signals by suppressing the spectral content of the distorted signal above the original signal bandwidth by means of adaptive nonlinear filtering. The nonlinear compensator is constructed using a power series filter with adaptive coefficients. The adaptive coefficients are identified blindly by applying a least-squares criterion to the out-of-band spectral content of the nonlinear compensator output. The extraction of the out-of-band signal is efficiently performed by the discrete cosine transform. The effectiveness of the blind nonlinear compensation method is demonstrated by way of simulation examples involving periodic, colored noise, and bandlimited speech signals.     

Spread Spectrum System Using Noise Band Shift Keying

A new spread spectrum technique using band-limited Gaussian noise for transmission and incoherent detection at the receiver has been discussed. The proposed system called noise band shift keying (NBSK) may be considered as a modified form of the frequency-shift keying (FSK) system. In the NBSK system nonoverlapping bandlimited noise is transmitted instead of pure tones as in the FSK system and the center frequency of the noise is chosen on the basis of the binary data signal. For this system, an expression for the probability of error has been derived and it has been shown that its performance under nonfading channel conditions is identical to that of the FSK system with frequency diversity under Rayleigh fading conditions. Compared to the conventional spread spectrum systems, the proposed method is considerably more simple to implement and is attractive where adequate bandwidth is available.     

New Aspects of Electromagnetic Information Theory for Wireless and Antenna Systems

This paper investigates information-theoretic characterization, via Shannon's information capacity and number of degrees of freedom, of wave radiation (antenna) and wireless propagation systems. Specifically, the paper derives, from the fundamental physical point of view of Maxwell's equations describing electromagnetic fields, the Shannon information capacity of space-time wireless channels formed by electromagnetic sources and receivers in a known background medium. The theory is developed first for the case of sources working at a fixed frequency (time-harmonic case) and is expanded later to the more general case of temporally bandlimited systems (time-domain fields). In the bandlimited case we consider separately the two cases of time-limited and essentially bandlimited systems and of purely bandlimited systems. The developments take into account the physical radiated power constraint in addition to a constraint in the source $L^{2}$ norm which acts to avoid antenna superdirectivity. Based on such radiated power and current $L^{2}$ norm constraints we derive the Shannon information capacity of canonical wireless and antenna systems in free space, for a given additive Gaussian noise level, as well as an associated number of degrees of freedom resulting from such capacity calculations. The derived results also illustrate, from a new information-theoretic point of view, the transition from near to far fields.      

Bandlimited extrapolation using time-bandwidth dimension

The problem of extrapolating discrete-index bandlimited signals from a finite number of samples is addressed in this paper. The algorithm presented in this paper exploits the fact that the set of bandlimited signals that are also essentially time-limited is approximated well by a low-dimensional linear subspace. This fact, which is well known for one-dimensional (1-D) signals with contiguous passbands and time-concentration intervals, is established for a more general class of multidimensional (m-D) signals with discontiguous passbands and discontiguous time-concentration regions. A criterion is presented for determining the dimension of the approximating subspace and the minimax optimal subspace itself based on knowledge of the passband, time-concentration regions, energy concentration factor, and bounds on the tolerable extrapolation error. The extrapolation is constrained to lie in this subspace, and parameters characterizing the extrapolation are obtained from the data by solving a linear system of equations. For certain sampling patterns, the system is ill conditioned, and a second rank reduction is needed to reduce the deleterious effects of observation noise and modeling error. A novel criterion for rank selection based on known bounds on noise power and modeling error is presented. The effectiveness of the new algorithm and the rank selection criterion are demonstrated by means of computer simulations     

Efficient Pulse Shaping Using MSK or PSK Modulation

The increasing requirement for high data rate, bandwidth efficient digital radio systems has led to the development of MSK-type modulation methods designed to achieve a compact signal spectrum. These modulation methods include sinusoidal frequency shift keying (SFSK), special MSK-type pulse shapes, and multiamplitude minimum shift keying (MAMSK). When more compact signal spectra are required, bandlimited filtering must be introduced. This note considers the use of conventional MSK or PSK modulators followed by newly developed bandlimited pulse shaping filters. With this approach, it is shown that MSK and offset QPSK modulators yield identical signals on the channel when filtered by properly designed bandlimited pulse shaping networks.     

Fitting a bandlimited signal to given points

One of the fundamental problems in communications is the transmission of a signal through a bandlimited channel. It should, therefore, be of great interest to find a general method of transmitting an arbitrarily close approximation to any finite signal through a channel which is arbitrarily bandlimited. The present paper develops such a method and evaluates the cost in time and energy to accomplish this feat. The problem of fitting an arbitrarily bandlimited signal to a finite number of arbitrary points is solved, and the minimum energy signal, fitting the points and having a spectrum confined to the given pass band, is found. The behavior of this signal, with shrinking bandwidth, is investigated.     

Debye Function Expansions of Complex Permittivity Using a Hybrid Particle Swarm-Least Squares Optimization Approach

With appropriate modifications, the finite-difference time-domain (FDTD) method can be used to analyze propagation through linear isotropic dispersive media. Although materials characterized by the Debye permittivity model can be analyzed accurately and efficiently using well established methods, the treatment of other types of frequency dependence is more difficult. This paper proposes the use of a weighted sum of Debye functions to approximate more general complex permittivity functions. A combination of the particle swarm optimization method and linear least squares optimization is used to find the relaxation frequencies and weights in the expansion, which can then be accommodated in the FDTD method using one of the established methods. Two key advantages of the proposed approach are that the relaxation frequencies are bandlimited and the weights are always positive. These two characteristics help to maintain the accuracy and stability of the FDTD solution. It is also shown that the correlation between the imaginary parts of two Debye functions is the same as that between the real parts.     

Chip Pulse Shaping in Asynchronous Chaos-Based DS-CDMA

This paper extends and fully formalizes some previous results by developing an analytical method to account for the general chip pulse for DS-CDMA systems in an asynchronous environment with an integrate-and-dump receiver, applying it to commonly used pulses. Given the pulse, such a formal method allows us to define the optimum spreading code autocorrelation to be used and the relative signal-to-interference ratio performance. A chaos-based spreading code is plugged into this model to show that such an optimum performance can be very well approximated by practical sequence generators. This is shown by analyzing some typical bandlimited and substantially bandlimited pulses and determining the optimum spreading for each of them. These results prove that the gain of chaos-based spreading over conventional i.i.d.-like spreading can reach 75% when practical bandlimited pulses are considered.     

基于椭圆球面波函数(PSWF)的基带传输波形设计方法

针对基带传输中的码间串扰问题,提出了基于椭圆球面波函数的基带传输系统设计方法。基带传输波形采用频带近似有限、持续时间为一个码元长度的椭圆球面波函数,根据基带传输系统的传输速率、码元持续时间、传输带宽等系统要求设置椭圆球面波函数的参数,通过构建椭圆球面波函数积分方程、数值求解和特征值排序等步骤完成基带传输波形设计。该方法不仅可有效提高基带传输系统的抗干扰能力,同时也使系统具有较好的功率利用率。     

Symmetry-constrained 3-D interpolation of viral X-raycrystallography data

A three-dimensional (3-D) interpolation problem that is important in viral X-ray crystallography is considered. The problem requires new methods because the function is known to have icosahedral symmetry, the data is corrupted by experimental errors and therefore lacks the symmetry, the problem is 3-D, the measurements are irregularly spaced, and the number of measurements is large (10⁴). A least-squares approach is taken using two sets of basis functions: the functions implied by a minimum-energy bandlimited exact interpolation problem and a complete orthonormal set of bandlimited functions. A numerical example of the Cowpea Mosaic Virus is described     

A Multilayer Optical Packet Switching Network Based on the Kautz Graph and Optical Passive Star Couplers

The multihop optical network is the most appropriate solution to satisfy the increasing applications of Internet services. This paper extends the regular Kautz graph to one with multiple layers in order to produce more architectural variations. The connectivity between adjacent layers utilizes the systematic connection patterns of a regular Kautz graph. A routing algorithm based on its property is presented. Optical passive star (OPS) couplers are adopted to implement our new topologies. Three scheduling criteria that can solve the contention problem in the intermediate nodes are evaluated and compared in terms of their capability to improve the accessibility.     

Blind adaptive equalization of mismatch errors in a time-interleaved A/D converter system

To significantly increase the sampling rate of an A/D converter (ADC), a time-interleaved ADC system is a good option. The drawback of a time-interleaved ADC system is that the ADCs are not exactly identical due to errors in the manufacturing process. This means that time, gain, and offset mismatch errors are introduced in the ADC system. These errors cause distortion in the sampled signal. In this paper, we present a method for estimation and compensation of the mismatch errors. The estimation method requires no knowledge about the input signal except that it should be bandlimited to the Nyquist frequency for the complete ADC system. This means that the errors can be estimated while the ADC is running. The method is also adaptive to slow changes in the mismatch errors. The estimation method has been validated with simulations and measurements from a time-interleaved ADC system.     

On Designing PAM Pulses Optimally Tolerant to Timing Jitter

This paper deals with the design of bandlimited baseband PAM pulses that are optimally tolerant to timing jitter in a maximally flat sense. In this design the bandwidth can be chosen arbitrarily. The resulting time responses are relatively insensitive to small amounts of timing jitter and so represent an optimal solution for this type of impairment. Analytic results are derived in the frequency domain after translating conditions on maximal flatness from the time domain into the frequency domain by means of the Poisson sum formula.     

Blind code-timing estimation for CDMA systems with bandlimited chip waveforms in multipath fading channels

In this paper, we present a blind code-timing estimator for asynchronous code-division multiple-access (CDMA) systems that use bandlimited chip waveforms. The proposed estimator first converts the received signal to the frequency domain, followed by a frequency deconvolution to remove the convolving chip waveform, and then calculates the code-timing estimate from the output of a narrowband filter with a sweeping center frequency, which is designed to suppress the overall interference in the frequency domain. The proposed estimator is near-far resistant, and can deal with time- and frequency-selective channel fading. It uses only the spreading code of the desired user, and can be adaptively implemented for both code acquisition and tracking. We also derive an unconditional Crame/spl acute/r-Rao bound (CRB) that is not conditioned on the fading coefficients or the information symbols. It is a more suitable lower bound than a conditional CRB for blind code-timing estimators which do not assume knowledge of the channel or information symbols. We present numerical examples to evaluate and compare the proposed and several other code-timing estimators for bandlimited CDMA systems.     

基于CORDIC算法的DDS实现

直接数字频率合成(DDS)技术在软件无线电方面有着广泛的应用,而坐标旋转数字计算方法(Coordinate Rotation Digital Computer,CORDIC)通过移位和加减运算代替乘法运算是构造DDS的一种理想的手段。介绍了CORDIC算法的基本原理,采用流水线方法对CORDIC算法进行了设计实现,用以取代传统的ROM查找表法。实验验证,基于CORDIC算法的DDS满足高速、高精度、高分辨率和实时运算的要求。     

Sampling of Bandlimited Signals in Fractional Fourier Transform Domain

Fractional Fourier transformed bandlimited signals are shown to form a reproducing kernel Hilbert space. Basic properties of the kernel function are applied to the study of a sampling problem in the fractional Fourier transform (FRFT) domain. An orthogonal sampling basis for the class of bandlimited signals in the FRFT domain is then given. A nonuniform sampling theorem for bandlimited signals in the FRFT domain is also presented. Numerical experiments are given to demonstrate the effectiveness of the proposed nonuniform sampling theorem.     

Quasi-bandlimited properties of Radon transforms and theirimplications for increasing angular sampling densities

The n-dimensional (n-D) radon transform, which forms the mathematical basis for a broad variety of tomographic imaging applications, can be viewed as an n-D function in n-D sinogram space. Accurate reconstruction of continuous or discrete tomographic images requires full knowledge of the Radon transform in the corresponding n-D sinogram space. In practice, however, one can have only a finite set of discrete samples of the Radon transform in the sinogram space. One often derives the desired full knowledge of the Radon transform from its discrete samples by invoking various interpolation algorithms. According to the Wittaker-Shannon sampling theorem, a necessary condition for a full and unique recovery of the Radon transform from its discrete samples is that the Radon transform itself be bandlimited. Therefore, it is necessary to analyze the bandlimited properties of the Radon transform. In this work, the authors analyze explicitly the bandlimited properties of the Radon transform and show that the Radon transform is mathematically quasi-bandlimited [or essentially bandlimited] in two quantitative senses and can essentially be treated as bandlimited in practice. The quasi-bandlimited properties can be used for increasing the angular sampling density of the Radon transform