浊音短时复倒谱的新模型及用于语音同态解卷积的研究

本文介绍一种浊音短时复倒谱的新模型，通过与传统模型的分析对比，提出了将该模型用于同态解卷积恢复声道冲激响应的新方法，并进行了实验研究。对解卷积中的问题进行了分析探讨。     

A multidimensional isomorphic operator and its properties-aproposal of finite-extent multidimensional cepstrum

We propose a new multidimensional homomorphic operator that replaces the conventional complex cepstrum transformation. We treat multidimensional signals of finite support since any signal we can actually observe and deal with is of finite support. We first show that for any sequence of finite support there exists a coordinate transformation that transforms the support of a given sequence into the first quadrant in the multidimensional signal space. We then propose a new multidimensional homomorphic operator Ψ which transforms a sequence of finite support into another sequence of finite support in the first quadrant. It is proved that the operator Ψ is an isomorphism between two multidimensional signal spaces of finite support where finite convolution and usual addition, respectively, are defined as binomial operations. It is also shown that unlike the conventional complex cepstrum, the proposed operator Ψ is quite simple to compute and requires no complicated procedure like phase unwrapping, while it maintains the special features of the conventional complex cepstrum transformation that are useful in homomorphic signal processing. Moreover we clarify some algebraic structure of the multidimensional signal space with the finite convolution as a binomial operation. Finally it is shown by a numerical example that the deconvolution system using the proposed operator Ψ gives a much better result than the conventional complex cepstrum method     

On homomorphic deconvolution of bandpass signals

A convolution may be represented as x(.)=r(.)* w(.). The goal of deconvolution is to extract r(.) and w(.) from a knowledge of x(.) and it finds numerous applications in digital signal processing. Of practical interest in oil exploration is the case where w(.) is a seismic pressure wavelet, x(.) is the observed seismic response, and r(.) is the reflectivity of the Earth. A number of procedures have been proposed, including predictive, deterministic, and homomorphic deconvolution. Homomorphic deconvolution has been found to be particularly efficient for those cases where x(.) is known to be fullband. This paper presents a robust constructive procedure for efficient homomorphic deconvolution for those cases where x(.) is a bandpass signal. Extensive comparisons with other methods for deconvolving bandpass signals on measured seismic data traces (including the Novaya Zemlya event) illustrate the improvement in the deconvolution     

基于修正自相关算法的THz-TDS聚乙烯测厚反卷积算法

在聚乙烯材料管道生产制造过程中,管道厚度精确测量是影响管道生产质量的一个重要技术问题,太赫兹非金属厚度透射测量过程中,通过测量两次透射信号的光程时间差与材料折射率计算得到样品厚度参数,为了准确提取两次透射信号的光程时间差值,需要对原始时域信号进行信号表征。通过高斯滤波反卷积得到脉冲响应函数表征时域信号已经成为了一种成熟且有效的技术手段。但一方面由于太赫兹波在聚乙烯材料中的传播存在明显的频散现象,同时其透射率高回波信号较弱,导致信噪比较低,在脉冲响应函数提取过程中放大了干扰信号的比重,造成信号失真、淹没,无法准确提取信号。本文通过对带通滤波后的时域信号采用修正型自相关算法进行自相关性分析,再结合高斯滤波反卷积运算,得到改进后的脉冲响应函数。旨在解决太赫兹非金属测量领域时域信号表征问题。改进算法实验结果显示加强了信号的清晰度,解决了因杂波信号干扰造成的脉冲响应信号失真或淹没情况,显著提高了脉冲响应信号信噪比。     

Time domain deconvolution of transient radar data

A simple technique is presented for obtaining the impulse response of a conducting radar target by deconvolving the measured response of the experimental system from the measured response of the target. The scheme uses singular value decomposition (SVD). It is shown that the ill-conditioned nature of the deconvolution process can be linked to the use of inappropriate frequency information in the representation of the unknown impulse response. Examples using measured transient radar data establish the usefulness of the scheme. The noise sensitivity of the deconvolution process can also be traced to the improper representation of the impulse response. Accurate deconvolution is demonstrated even in the presence of large amounts of random noise     

From frequency to quefrency: a history of the cepstrum

The idea of the log spectrum or cepstral averaging has been useful in many applications such as audio processing, speech processing, speech recognition, and echo detection for the estimation and compensation of convolutional distortions. To suggest what prompted the invention of the term cepstrum, this article narrates the historical and mathematical background that led to its discovery. The computations of earlier simple echo representations have shown that the spectrum representation domain results does not belong in the frequency or time domain. Bogert et al. (1963) chose to refer to it as quefrency domain and later termed the spectrum of the log of a time waveform as the cepstrum. The article also recounts the analysis of Al Oppenheim in relation to the cepstrum. It was in his theory for nonlinear signal processing, referred to as homomorphic systems, that the realization of the characteristic system of homomorphic convolution was reminiscent of the cepstrum. To retain both the relationship to the work of Bogart et al. and the distinction, the term power cepstrum was eventually applied to the nonlinear mapping in homomorphic deconvolution . While most of the terms in the glossary have faded into the background, the term cepstrum has survived and has become part of the digital signal processing lexicon.     

Nonparametric estimation of ultrasound pulses

An algorithm for nonparametric estimation of 1D ultrasound pulses in echo sequences from human tissues is derived. The technique is a variation of the homomorphic filtering technique using the real cepstrum, and the underlying basis of the method is explained. The algorithm exploits a priori knowledge about the structure of RF line echo data and can employ a number of adjacent RF lines from an image. The prime application of the algorithm is to yield a pulse suitable for deconvolution algorithms. This will enable these algorithms to properly take into account the frequency dependence of the attenuation and its variation within a patient and among patients. It is also possible to use the estimated pulse for attenuation estimation, and the consistency of the assumptions underlying the proposed technique is demonstrated by its ability to recover low variance attenuation estimates in the normal liver from in vivo pulse-echo data. Estimates are given for 8 different patients     

单通道带通信号的复基带盲解卷积算法

该文提出了一种基于多途信道单通道接收的带通数据(波束或传感器输出)自相关函数的盲解卷积算法。该算法先通过复解调将带通信号频谱搬移到0频率附近,然后进行低通滤波和降采样率,得到其复基带信号。再针对单通道复基带信号,以其自相关函数在零延时之外某区间内的实部平方和最小为准则,推导出复基带多途信号盲解卷积的LMS自适应迭代算法。该方法能够适用于带通高斯信号和非高斯信号,与基于高阶统计量的方法相比,对源信号概率分布具有较宽的适用面,计算机仿真结果验证了该方法的正确性。     

Mesure de la réponse impulsionnelle d’un milieu de transmission: application aux fibres optiques

The impulse response of multimode optical fibres is experimentally found using a time-domain measurement method whose basic performances are significantly improved by implementing an optimal and automatic deconvolution technique. A likelihood criterium is applied to the impulse response allowing the information to be extracted from the noise (constrained regression). The impulse response carries all the usefull information since its Fourier transform is the complex transfer function (amplitude and phase). Some experimental results are presented in order to illustrate this new method.     

Blind deconvolution of ultrasound sequences using nonparametric local polynomial estimates of the pulse

The problem of reconstructing the reflectivity of a biological tissue is examined by means of blind deconvolution of the echo ultrasound signals. It is shown that the quality of the reconstruction procedure can be significantly improved when initially the ultrasonic pulse is accurately estimated. A new approach to the estimation of the ultrasound pulse echo sequences is proposed, using local polynomial approximation, which is closely related to the wavelet transform theory. This approach can be viewed as a modification of homomorphic deconvolution, by using bases different from the Fourier basis of the space of square-integrable functions L2. The bases used here are the orthogonal compactly supported wavelet bases. It is shown that the locality of the estimate can be extremely useful in number of cases of practical interest, resulting in estimates with smaller root-mean squared (rms) errors, as compared with estimates employing the Fourier basis. This approach is applied to ultrasound signals, for estimation of the ultrasound pulse log-spectrum from the log-spectrum of radio-frequency (RF) sequences. It is shown, conceptually and experimentally, that the proposed approach can provide robust and rapidly computed estimates of the ultrasound pulses from the RF-sequences, as obtained in the process of tissue scanning. The pulse phase was recovered using the minimum-phase assumption, which was found to hold for the transducers in use. The obtained pulse estimates are used for the deconvolution of the RF-sequences, which result in stable estimates of the tissue reflectivity function, fairly independent of the properties of the imaging system. Simulated data, data obtained from several phantoms and from in vitro experiments have been processed and the results seem to be quite promising.     

Time-domain cepstral transformations

The realization of homomorphic systems for convolution is addressed, motivated by the limitations of the Fourier-transform-based method commonly used in homomorphic (complex cepstral) filtering. The time-domain cepstral transformation (TDCT) method, which is entirely based on time-domain calculations, thus avoiding or minimizing the problems associated with the FT method, is introduced. Explicit transformations of an ordinary mixed-phase time sequence (belonging to convolution space) into its complex cepstrum time sequence (belonging to additive cepstrum vector space) and vice versa are derived. The method does not require unwrapped phase calculations, and no specific windows are used to precondition the signal in order to produce a more accurate representation of the complex cepstrum. It trades reduced computational efficiency for improved performance. Examples comparing Fourier-based and TD cepstrum transformations are presented     

一种基于倒谱分析的抗多径衰落的算法

本文提出一种基于复倒谱分析和同态滤波技术来对抗多径传播引起的衰落的算法。该算法通过在倒谱域滤波实现了对多径分量的有效抑制。文中给出了算法的理论推导过程及实验设计方法,并进行了计算机仿真。结果表明,本算法能有效减小衰落信号与原信号间的均方误差,改善多径衰落信道的传输质量。     

The cross-bicepstrum: definition, properties, and application forsimultaneous reconstruction of three nonminimum phase signals

The recovery of three signals from their cross-bispectrum (or the identification of the impulse responses of three parallel linear time-invariant (LTI) systems from the cross-bispectrum of their system outputs) by computing the complex cepstrum of the cross-bispectrum, as long as the signals (or impulse responses) have no zeros on the unit circle, is discussed. It is shown that the three signals can be separated completely and (approximately) recovered in the cross-bicepstrum domain, except for their magnitude and linear phase factors. The computation of the cross-bicepstrum can be seen as a method for the simultaneous computation of the ordinary complex cepstra of three nonminimum-phase signals without the need for phase unwrapping. Both least-squares and fast Fourier-transform (FFT)-based methods for computing the bicepstral coefficients are presented. Simulation examples of signal reconstruction in Gaussian white and nonGaussian colored noise and of system identification are included. The results are extended to nth-order cross-spectra, and the factorization problem for these spectra is discussed     

Subsurface radar signal deconvolution

We present two methods of signal deconvolution for systems whose impulse response (wavelet function) can be explicitly determined, and where the goal is to locate short impulses in the presence of strong, reverberation-like interferences.The first method, which we call algebraic deconvolution, differs from other known techniques in two ways: first of all, explicit use of the wavelet function provides more powerful a priori knowledge than the autocorrelation or the power spectrum. Secondly, this method permits to flexibly trade off noise versus resolution.In the second method presented here, we use an analytical model (synthetic wavelet) of the system impulse response to determine an inverse filter.These methods have been developed for video pulse radar signals, and encouraging early results have been obtained.     

Time-domain macromodel of planar microwave devices by FDTD andmoment expansion

The microwave design of highly complex systems can be addressed by segmentation techniques. To this purpose, a subsystem macromodel, such as the impulse response matrix, needs to be computed in an accurate and efficient way. In this paper, we present a combined procedure, based on finite-difference time-domain and a moment-expansion deconvolution by which the impulse response matrix is obtained via time-domain processing only. The algorithm has been tested on microwave planar devices with satisfactory accuracy     

Application of Homomorphic Deconvolution to Dilution Curves

The application of a homomorphic deconvolution technique to indicator dilution curves is investigated. An indicator dilution curve with recirculation is decomposed into the primary circulation and the first recirculation components by homomorphic filtering. First, the method is applied to a simple model in which a dilution curve with recirculation is represented by mathematical functions. The assumed mean transit time and shunt fraction are determined from the two decomposed curves. Second, the method is applied to real data, i.e., the pulmonary time-activity curves from radionuclide angiocardiography. Pulmonary-to-systemic flow ratios are calculated from the areas of two decomposed curves and compaxed with those from cardiac catheterization. It may be concluded that homomorphic deconvolution seems to be a possible method of recovery of the primary circulation curve and also of the first recirculation curve from an indicator dilution curve with recirculation.     

Principles of high-resolution radar based on nonsinusoidal waves.III. Radar-target reflectivity model

For pt.II see ibid., vol.31, no.4, p.369-75 (1989). A target-reflectivity model is developed for carrier-free nonsinusoidal waves with the time variation of a Gaussian pulse or a sequence of positive and negative Gaussian pulses representing a binary code, as was introduced in pt.I (see ibid., vol.31, no.4, p.359-68 (1989)). It is shown that the impulse response of a complex target that is composed of a finite number of scattering centers can be expressed as a sequence of Gaussian pulses. The characteristics of the Gaussian pulses, e.g. peak amplitude and nominal duration, are functions of the physical properties of the scattering centers, which are unique for each target. Hence, the impulse response waveform of a target can be regarded as a one-dimensional image in time (or range), which is valuable information for target classification and recognition. A signal processing technique is developed for obtaining an approximation of a target impulse response waveform from the backscattered and received signals. The signal processor is specifically developed for radar signals with the structure of complementary code pairs whose autocorrelation function is a single narrow pulse with no time sidelobes     

A phase reconstruction algorithm from bispectrum [seismicreflection data]

A computationally efficient procedure for the reconstruction of the impulse response of a (minimum- or nonminimum-phase) linear time-invariant system from its bispectrum is presented. This method is based on computing cepstrum of the impulse response sequence from the ω₁=ω₂ slice of the bispectrum. The algorithm can be implemented by using only the one-dimensional fast Fourier transform algorithm     

On the derivatives of the homomorphic transform operator and theirapplication to some practical signal processing problems

The derivatives of the homomorphic transform operator and its inverse are obtained with Banach algebra techniques. The derivatives can be applied to two important practical problems. The first problem involves a standard method for designing recursive multidimensional digital filters. The method uses spectral factorization or Hilbert transform methods to stabilize a given weighting sequence without changing its magnitude response in the frequency domain. The derivatives of the stabilization process are required by the design algorithm. The derivatives of the homomorphic transform, together with the chain rule for Frechet derivatives, can be used to calculate the derivatives of stabilization analytically. The second problem is the analysis of homomorphic deconvolution techniques in the presence of additive disturbances. The fact that the homomorphic transform maps convolution to addition makes it very useful in certain blind deconvolution problems. However, the highly nonlinear nature of the homomorphic transform complicates analysis of the effects of additive disturbances. In most practical applications, the presence of additive measurement noise is to be expected. The derivatives obtained in this paper are shown to be very useful in obtaining approximations of the effects of additive disturbances