The recovery of distorted bandlimited almost-periodic signals

It is shown that thePQ theorem can be used to solve a certain signal recovery problem in which the transmitted and received signals are almost periodic functions. In this problem the signal to be recovered, which is bandlimited, is nonlinearly distorted and then bandlimited to the original band. Related signal recovery results are also given. These related results, unlike thePQ theorem, are applicable in settings in which the underlying signal space is not a Hilbert space or even a space that is complete.     

Perfect recovery and sensitivity analysis of time encoded bandlimited signals

A time encoding machine is a real-time asynchronous mechanism for encoding amplitude information into a time sequence. We investigate the operating characteristics of a machine consisting of a feedback loop containing an adder, a linear filter, and a noninverting Schmitt trigger. We show that the amplitude information of a bandlimited signal can be perfectly recovered if the difference between any two consecutive values of the time sequence is bounded by the inverse of the Nyquist rate. We also show how to build a nonlinear inverse time decoding machine (TDM) that perfectly recovers the amplitude information from the time sequence. We demonstrate the close relationship between the recovery algorithms for time encoding and irregular sampling. We also show the close relationship between time encoding and a number of nonlinear modulation schemes including FM and asynchronous sigma-delta modulation. We analyze the sensitivity of the time encoding recovery algorithm and demonstrate how to construct a TDM that perfectly recovers the amplitude information from the time sequence and is trigger parameter insensitive. We derive bounds on the error in signal recovery introduced by the quantization of the time sequence. We compare these with the recovery error introduced by the quantization of the amplitude of the bandlimited signal when irregular sampling is employed. Under Nyquist-type rate conditions, quantization of a bandlimited signal in the time and amplitude domains are shown to be largely equivalent methods of information representation.     

Limits on bandlimited signals

The problem of estimating the errors arising in a variety of numerical operations involving bandlimited functions is considered. The errors are viewed as responses of suitably created systems, and the analysis is based on the evaluation of the maximum response of these systems in terms of the energy or power of their input. The investigation includes deterministic and random signals, and it is extended to two-dimensional functions and Hankel transforms. Finally, the results are related to the uncertainty principle in one and two variables.     

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.     

Algorithm for complex-zero location of real bandlimited signals

A computationally efficient algorithm for locating complex zeros of real bandlimited signals is discussed. The amount of processing is minimal rendering the algorithm suitable for real time applications. The performance of the algorithm is evaluated for test signals by computer simulation and some results are presented     

Nonparametric bispectrum-based time delay estimation for bandlimited signals

Modifications to an existing nonparametric, bispectrum-based approach are presented to handle the estimation of differential time delays for bandlimited non-Gaussian signals given signal measurements at two spatially separated sensors. It is shown that unlike the existing approaches, it is not necessary to consider the measurement auto- and cross-bispectrum over the entire two-dimensional (normalised) frequency domain of 0 to 1; rather, a smaller subset suffices     

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.     

频带有限信号非一致采样重建的谱方法

本文研究带限信号的非一致采样重建问题。我们利用信号频带分割方法,导出带限信号周期非一致采样情 况下的具体重建公式,并由此给出带限信号有限采样在区间上的插值公式并对它进行了数值实验。最后利用频谱分割方法, 讨论了多带限信号一些采样策略。     

Optimal reconstruction of bandlimited bounded signals

A formula is presented for restoring bounded, bandlimited signals from a finite number of samples. The restoration is linear in the samples used, and the error bound of the method is the theoretical minimum.     

General relations for nonperiodic bandlimited signals in three-dimensional electron flow

Relations for bandlimited signals in electron flow are presented that may be considered as a generalisation of power relations for sinusoidal signals. Inequalities defining limiting values for the power densities are obtained when signals exist in three frequency bands only which correspond to the frequencies in a parametric amplifier.     

Moving average restoration of bandlimited signals from noisyobservations

The purpose of this paper is to describe the extension of the Whittaker-Shannon sampling theorem to reconstruction of bandlimited functions in the presence of zero mean, uncorrelated noise. It is shown that the classical Whittaker-Shannon sampling scheme is not consistent in the case of noisy measurements, and new reconstruction algorithms based on the moving average smoothing are proposed. The weak and strong consistency of the algorithms is established, and the rate of convergence is investigated. The theory is verified in the computer simulations     

联合迭代滤波与压扩参数优化的OFDM信号峰平比抑制

针对现有基于压扩变换处理的信号峰平比抑制方法性能单一且参数固定等缺陷,提出一种联合迭代滤波与自适应压扩参数优化的OFDM信号峰平比抑制方案。该方案能够同时对信号的峰平比PAPR和接收端误码率BER性能进行联合优化,并在迭代过程中有效消除因信号幅度畸变所引起的带外频谱再生;所提信号压扩及解压扩函数形式简单,计算复杂度较小;推导并给出了该方案可获得的PAPR抑制增益和BER理论性能界。仿真结果表明,该方案可同时获得较好的信号PAPR抑制、误码率以及带外功率谱性能,并在迭代过程中对压扩参数进行自适应调整,能够有效提高算法的适用灵活性。     

Distance measures for viterbi decoding of coded and bandlimited 8PSK signals

The paper studies a digital modem that transmits a convolutionally encoded eight-phase-shift keyed (CE8PSK) signal over a satellite channel and employs a near-maximum-likelihood decoder at the receiver. Several different earth-stations are assumed to have simultaneous access to a given transponder in the satellite as an arrangement of frequency-division multiple access. Adjacent channel interference (ACI) is neglected here. The high-power amplifier (HPA) at the earth-station transmitter and the satellite transponder are assumed to be linear. The channel distorts the data signal, through the bandlimiting introduced by the equipment filters, and it adds stationary white Gaussian noise to the data signal at the receiver input. The resulting noisy and distorted data signal is coherently demodulated. Four different bandwidths of the transmitted CE8PSK signal are considered, together with three different demodulation processes. The decoder uses the Viterbi algorithm, together with one of six different distance measures to determine the costs of the stored vectors (survivors). The paper describes the various techniques involved in the modem, and presents the results of an extensive series of computer-simulation tests to measure the performances of the system with all appropriate combinations of the signal bandwidth, demodulation process and distance measure. The results of the tests are then used to determine the preferred modem design.     

Filterbank reconstruction of bandlimited signals from nonuniformand generalized samples

This paper introduces a filterbank interpretation of various sampling strategies, which leads to efficient interpolation and reconstruction methods. An identity, which is referred to as the interpolation identity, is developed and is used to obtain particularly efficient discrete-time systems for interpolation of generalized samples as well as a class of nonuniform samples, to uniform Nyquist samples, either for further processing in that form or for conversion to continuous time. The interpolation identity also leads to new sampling strategies including an extension of Papoulis' (1977) generalized sampling expansion     

Sampling of bandlimited signals in the linear canonical transform domain

The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. This paper investigates the sampling of bandlimited signals in LCT domain. First, we propose the linear canonical series (LCS) based on the LCT, which is a generalized pattern of Fourier series. Moreover, the LCS inherits all the nice properties from the LCT. Especially, the Parseval’s relation is presented for the LCS, which is used to derive the sampling theorem of LCT. Then, utilizing the generalized form of Parseval’s relation for the complex LCS, we obtain the sampling expansion for bandlimited signals in LCT domain. The advantage of this reconstruction method is that the sampling expansion can be deduced directly not based on the Shannon theorem.     

Synthesis of bandlimited signals with independent amplitude and phase modulation

The synthesis of a bandpass bandlimited signal with independent AM and PM channels is considered, where the bandwidth of each of the two information signals is required to be less than or equal to half the bandwidth of the bandpass signal. A simple iterative algorithm for generation of the bandpass signal is proposed, and sample results are presented. It is shown that this approach may be useful in simultaneous amplitude phase transmission systems even when the number of iterations is small.     

On the performance of iterative noncoherent detection of codedM-PSK signals

Differential encoding is often used in conjunction with noncoherent demodulation to overcome carrier phase synchronization problems in communication systems employing M-ary phase-shift keying (M-PSK). It is generally acknowledged that differential encoding leads to a degradation in performance over absolutely encoded M-PSK systems with perfect carrier synchronization. In this paper, we show that when differential encoding is combined with convolutional encoding and interleaving, this degradation does not necessarily occur. We propose a novel noncoherent receiver for differentially encoded M-PSK signals that is capable of significantly outperforming optimal coherent receivers for absolutely encoded M-PSK using the same convolutional code. This receiver uses an iterative decoding technique and is based on a multiple differential detector structure to overcome the effect of the carrier phase error. In addition, to better illustrate the benefits of the powerful combination of convolutional encoding, interleaving, and differential encoding, we also present an iterative coherent receiver for differentially encoded M-PSK     

Reconstruction of multidimensional bandlimited signals from nonuniform and generalized samples

This paper addresses the problem of multidimensional signal reconstruction from nonuniform or generalized samples. Typical solutions in the literature for this problem utilize continuous filtering. The key result of the current paper is a multidimensional "interpolation" identity, which establishes the equivalence of two multidimensional processing operations. One of these uses continuous domain filters, whereas the other uses discrete processing. This result has obvious benefits in the context of the afore mentioned problem. The results here expand and generalize earlier work by other authors on the one-dimensional (1-D) case. Potential applications include two-dimensional (2-D) images and video signals.