Comparison between complex amplitude envelope representation and complex analytic signal representation in studying pulsed Gaussian beam

Analytic propagation expressions of pulsed Gaussian beam are deduced by using complex amplitude envelope representation and complex analytic signal representation. Numerical calculations are given to illustrate the differences between them. The results show that the major difference between them is that there exists singularity in the beam obtained by using complex amplitude envelope representation. It is also found that singularity presents near propagation axis in the case of broadband and locates far from propagation axis in the case of narrowband. The critical condition to determine what representation should be adopted in studying pulsed Gaussian beam is also given. (C) 2004 Elsevier B.V. All rights reserved.

A Technique to Compute Smooth Amplitude, Phase, and Frequency Modulations From the Analytic Signal

Gabor's analytic signal (AS) is a unique complex signal corresponding to a real signal, but in general, it admits infinitely-many combinations of amplitude and frequency modulations (AM and FM, respectively). The standard approach is to enforce a non-negativity constraint on the AM, but this results in discontinuities in the corresponding phase modulation (PM), and hence, an FM with discontinuities particularly when the underlying AM-FM signal is over-modulated. In this letter, we analyze the phase discontinuities and propose a technique to compute smooth AM and FM from the AS, by relaxing the non-negativity constraint on the AM. The proposed technique is effective at handling over-modulated signals. We present simulation results to support the theoretical calculations.

Fractional Hilbert transform extensions and associated analytic signal construction

The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations. (C) 2013 Elsevier B.V. All rights reserved.

A Generalized Approach to Multiresolution Complex SAR Signal Processing

Multiresolution synthetic aperture radar (SAR) image formation has been proven to be beneficial in a variety of applications such as improved imaging and target detection as well as speckle reduction. SAR signal processing traditionally carried out in the Fourier domain has inherent limitations in the context of image formation at hierarchical scales. We present a generalized approach to the formation of multiresolution SAR images using biorthogonal shift-invariant discrete wavelet transform (SIDWT) in both range and azimuth directions. Particularly in azimuth, the inherent subband decomposition property of wavelet packet transform is introduced to produce multiscale complex matched filtering without involving any approximations. This generalized approach also includes the formulation of multilook processing within the discrete wavelet transform (DWT) paradigm. The efficiency of the algorithm in parallel form of execution to generate hierarchical scale SAR images is shown. Analytical results and sample imagery of diffuse backscatter are presented to validate the method.

On Computing Amplitude, Phase, and Frequency Modulations Using a Vector Interpretation of the Analytic Signal

The amplitude-modulation (AM) and phase-modulation (PM) of an amplitude-modulated frequency-modulated (AM-FM) signal are defined as the modulus and phase angle, respectively, of the analytic signal (AS). The FM is defined as the derivative of the PM. However, this standard definition results in a PM with jump discontinuities in cases when the AM index exceeds unity, resulting in an FM that contains impulses. We propose a new approach to define smooth AM, PM, and FM for the AS, where the PM is computed as the solution to an optimization problem based on a vector interpretation of the AS. Our approach is directly linked to the fractional Hilbert transform (FrHT) and leads to an eigenvalue problem. The resulting PM and AM are shown to be smooth, and in particular, the AM turns out to be bipolar. We show an equivalence of the eigenvalue formulation to the square of the AS, and arrive at a simple method to compute the smooth PM. Some examples on synthesized and real signals are provided to validate the theoretical calculations.

Binaural Signal Processing Motivated Generalized Analytic Signal Construction and AM-FM Demodulation

Binaural hearing studies show that the auditory system uses the phase-difference information in the auditory stimuli for localization of a sound source. Motivated by this finding, we present a method for demodulation of amplitude-modulated-frequency-modulated (AM-FM) signals using a ignal and its arbitrary phase-shifted version. The demodulation is achieved using two allpass filters, whose impulse responses are related through the fractional Hilbert transform (FrHT). The allpass filters are obtained by cosine-modulation of a zero-phase flat-top prototype halfband lowpass filter. The outputs of the filters are combined to construct an analytic signal (AS) from which the AM and FM are estimated. We show that, under certain assumptions on the signal and the filter structures, the AM and FM can be obtained exactly. The AM-FM calculations are based on the quasi-eigenfunction approximation. We then extend the concept to the demodulation of multicomponent signals using uniform and non-uniform cosine-modulated filterbank (FB) structures consisting of flat bandpass filters, including the uniform cosine-modulated, equivalent rectangular bandwidth (ERB), and constant-Q filterbanks. We validate the theoretical calculations by considering application on synthesized AM-FM signals and compare the performance in presence of noise with three other multiband demodulation techniques, namely, the Teager-energy-based approach, the Gabor's AS approach, and the linear transduction filter approach. We also show demodulation results for real signals.

Characteristics of the complex received signal in dynamic body area networks

This paper investigates the characteristics of the complex received signal in body area networks for two environments at the opposite ends of the multipath spectrum at 2.45 GHz. Important attributes of the complex channel such as the Gaussianity of the quadrature components and power imbalance, which form the basis of many popular fading models, are investigated. It is found that in anechoic environments the assumption of Gaussian distributed quadrature components will not always yield a satisfactory fit. Using a complex received signal model which considers a non-isotropic scattered signal contribution along with the presence of an optional dominant signal component, we use an autocorrelation function originally derived for mobile-to-mobile communications to model the temporal behavior of a range of dynamic body area network channels with considerable success. In reverberant environments, it was observed that the real part of the complex autocorrelation function for body area network channels decayed slightly quicker than that expected in traditional land mobile channels. © 2013 IEEE.

Characterization of a complex chemosensory signal transduction system which controls twitching motility in Pseudomonas aeruginosa

Virulence of the opportunistic pathogen Pseudomonas aeruginosa involves the coordinate expression of a wide range of virulence factors including type IV pili which are required for colonization of host tissues and are associated with a form of surface translocation termed twitching motility. Twitching motility in P. aeruginosa is controlled by a complex signal transduction pathway which shares many modules in common with chemosensory systems controlling flagella rotation in bacteria and which is composed, in part, of the previously described proteins PilG, PilH, PilI, PilJ and PilK. Here we describe another three components of this pathway: ChpA, ChpB and ChpC, as well as two downstream genes, ChpD and ChpE, which may also be involved. The central component of the pathway, ChpA, possesses nine potential sites of phosphorylation: six histidine-containing phosphotransfer (HPt) domains, two novel serine- and threonine-containing phosphotransfer (SPt, TPt) domains and a CheY-like receiver domain at its C-terminus, and as such represents one of the most complex signalling proteins yet described in nature. We show that the Chp chemosensory system controls twitching motility and type IV pili biogenesis through control of pili assembly and/or retraction as well as expression of the pilin subunit gene pilA. The Chp system is also required for full virulence in a mouse model of acute pneumonia.

洛仑兹脉冲光束的复振幅包络解和复解析信号解的比较研究

使用复振幅包络表示式和复解析信号表示式推导了洛仑兹脉冲光束的传输公式．通过具体数值计算对脉冲光束的复振幅包络解和复解析信号解在不同带宽时的传输进行了对比研究．数值结果表明脉冲光束为窄带时，在传输方向轴中心的一定范围内两种解是一致的，而对于宽带脉冲光束，复振幅包络解在轴中心较近的距离即表现出奇异性，复解析信号解才是符合物理意义的表示式．由数值计算得出了选择脉冲光束研究方法的条件，并从所得公式对复振幅包络解出现奇异性的现象进行了解释．

Is complex signal processing for bone conduction hearing aids useful?

OBJECTIVES To establish whether complex signal processing is beneficial for users of bone anchored hearing aids. METHODS Review and analysis of two studies from our own group, each comparing a speech processor with basic digital signal processing (either Baha Divino or Baha Intenso) and a processor with complex digital signal processing (either Baha BP100 or Baha BP110 power). The main differences between basic and complex signal processing are the number of audiologist accessible frequency channels and the availability and complexity of the directional multi-microphone noise reduction and loudness compression systems. RESULTS Both studies show a small, statistically non-significant improvement of speech understanding in quiet with the complex digital signal processing. The average improvement for speech in noise is +0.9 dB, if speech and noise are emitted both from the front of the listener. If noise is emitted from the rear and speech from the front of the listener, the advantage of the devices with complex digital signal processing as opposed to those with basic signal processing increases, on average, to +3.2 dB (range +2.3 … +5.1 dB, p ≤ 0.0032). DISCUSSION Complex digital signal processing does indeed improve speech understanding, especially in noise coming from the rear. This finding has been supported by another study, which has been published recently by a different research group. CONCLUSIONS When compared to basic digital signal processing, complex digital signal processing can increase speech understanding of users of bone anchored hearing aids. The benefit is most significant for speech understanding in noise.

Instantaneous phase of the autocorrelation and robustness to signal-dependent noise

The phase of an analytic signal constructed from the autocorrelation function of a signal contains significant information about the shape of the signal. Using Bedrosian's (1963) theorem for the Hilbert transform it is proved that this phase is robust to multiplicative noise if the signal is baseband and the spectra of the signal and the noise do not overlap. Higher-order spectral features are interpreted in this context and shown to extract nonlinear phase information while retaining robustness. The significance of the result is that prior knowledge of the spectra is not required.

Some new results on signal reconstruction from Fourier transform magnitude spectrum

We address the problem of signal reconstruction from Fourier transform magnitude spectrum. The problem arises in many real-world scenarios where magnitude-only measurements are possible, but it is required to construct a complex-valued signal starting from those measurements. We present some new general results in this context and show that the previously known results on minimum-phase rational transfer functions, and recoverability of minimum-phase functions from magnitude spectrum, form special cases of the results reported in this paper. Some simulation results are also provided to demonstrate the practical feasibility of the reconstruction methodology.

Event-triggered sampling using signal extrema for instantaneous amplitude and instantaneous frequency estimation

Event-triggered sampling (ETS) is a new approach towards efficient signal analysis. The goal of ETS need not be only signal reconstruction, but also direct estimation of desired information in the signal by skillful design of event. We show a promise of ETS approach towards better analysis of oscillatory non-stationary signals modeled by a time-varying sinusoid, when compared to existing uniform Nyquist-rate sampling based signal processing. We examine samples drawn using ETS, with events as zero-crossing (ZC), level-crossing (LC), and extrema, for additive in-band noise and jitter in detection instant. We find that extrema samples are robust, and also facilitate instantaneous amplitude (IA), and instantaneous frequency (IF) estimation in a time-varying sinusoid. The estimation is proposed solely using extrema samples, and a local polynomial regression based least-squares fitting approach. The proposed approach shows improvement, for noisy signals, over widely used analytic signal, energy separation, and ZC based approaches (which are based on uniform Nyquist-rate sampling based data-acquisition and processing). Further, extrema based ETS in general gives a sub-sampled representation (relative to Nyquistrate) of a time-varying sinusoid. For the same data-set size captured with extrema based ETS, and uniform sampling, the former gives much better IA and IF estimation. (C) 2015 Elsevier B.V. All rights reserved.

On the Distribution of Signal Phase in Body Area Networks

In this letter, we investigate the distribution of the phase component of the complex received signal observed in practical experiments using body area networks. Two phase distributions, the recently proposed kappa-mu and eta-mu probability densities, which together encompass the most widely used fading models, namely Semi-Gaussian, Rayleigh, Hoyt, Rice, and Nakagami-m, have been compared with measurement data. The kappa-mu distribution has been found to provide the best fit over a range of on-body links, while the user was mobile. The experiments were carried out in two dissimilar indoor environments at opposite ends of the multipath spectrum. It has also been found that the uniform phase distribution has not arisen in anyone of the experiments.

Signal-flow graphs: Direct method of reduction and MATLAB implementation

Block diagrams and signal-flow graphs are used to represent and to obtain the transfer function of interconnected systems. The reduction of signal-flow graphs is considered simpler than the reduction of block diagrams for systems with complex interrelationships. Signal-flow graphs reduction can be made without graphic manipulations of diagrams, and it is attractive for a computational implementation. In this paper the authors propose a computational method for direct reduction of signal-flow graphs. This method uses results presented in this paper about the calculation of literal determinants without symbolic mathematics tools. The Cramer's rule is applied for the solution of a set of linear equations, A program in MATLAB language for reduction of signal-flow graphs with the proposed method is presented.