Giovanni Jacovitti

Discrete time techniques for time delay estimation

Basic aspects of time delay estimation (TDE) based on sampled signals are investigated. The direct cross-correlation method is analyzed and compared to the average square difference function (ASDF) and the (addition only based) average magnitude difference function (AMDF) estimators, Their relative accuracy is theoretically evaluated, and previous empirical results are explained. It is shown that both the ASDF- and the AMDF-based estimators outperform the direct cross-correlation based estimator for medium-high signal-to-noise ratios. Moreover, the AMDF-based estimator, which avoids any multiplications, significantly reduces the computational complexity of the estimation procedure while offering only a moderate performance loss with respect to the ASDF based estimator. >

Multiresolution circular harmonic decomposition

A dictionary of complex waveforms suited for multiresolution analysis and individually steerable by multiplication by a complex factor is presented. It is based on circular harmonic wavelets (CHW) and is useful for pattern analysis under rotations. The main theoretical aspects of CHWs are illustrated, and an example of application to motion estimation is provided.

Texture synthesis-by-analysis with hard-limited Gaussian processes

A twin stage texture synthesis-by-analysis method is presented. It aims to approximate first- and second-order distributions of the texture, accordingly to the Julesz conjecture. In the first stage, the binary textural behavior of a given prototype is represented by means of a hard-limited Gaussian process. In the second stage, the texture is synthesized by passing the binary hard-limited Gaussian process through a linear filter followed by a zero memory histogram equalizer.

Methods for estimating the autocorrelation function of complex Gaussian stationary processes

New methods for estimating the autocorrelation function (acf) of a complex Gaussian stationary process are presented. These methods are based on a general invariance property for the autocorrelation of a common class of the above processes. This property suggests estimation procedures based on magnitude hard limiting and phase quantization. The procedures are an extension of the relay estimator, currently employed for real processes. The computational cost and the general properties of the methods are discussed. In particular, some estimators especially suited for very simple implementations are considered. The performance of the complex hybrid sign estimator is evaluated and compared to that of the classical Direct estimator. The proposed methods are attractive for many applications in the field of digital signal processing.

Estimation of the autocorrelation function of complex Gaussian stationary processes by amplitude clipped signals

The normalized autocorrelation function of a Gaussian process may be recovered from second order moments of their polarity, through the arcsin law. By analogy, it is possible to calculate the normalized autocorrelation function of a circularly complex Gaussian process from the knowledge of moments of its instantaneous phase. In the present paper, two estimators of the normalized autocorrelation function based on the phase only are presented. Their theoretical accuracy is evaluated and compared to the accuracy of the direct estimate. >

On a fast digital method of estimating the autocorrelation of a gaussian stationary process

The zero-mean stationary Gaussian processes have the property that if they are input into an instantaneous nonlinear device, the cross correlation of input and output is proportional to the auto-correlation of the input. This suggests an estimation procedure for the autocorrelation function based mainly on additions, which is a modified type of the PCC (polarity coincidence correlator). The object of this paper is to compute the bias and the variance of such an estimator and to discuss some fundamental properties. As a reference, some examples are provided which compare the behavior of the modified PPC estimator to the classical one based on products and additions.

Multiscale image features analysis with circular harmonic wavelets

In this contribution we introduce a new family of wavelets named Circular Harmonic Wavelets (CHW), suited for multiscale feature-based representations, that constitute a basis for general steerable wavelets. The family is based on Circular Harmonic Functions (CHF) derived by the Fourier expansion of local Radial Tomographic Projections. A multiscale general feature analysis can be performed by linearly combining the outputs of CHW operators of different order. After a survey on the general properties of the CHFs, we investigate the relationship between CHF and the wavelet expansion, stating the basic admissibility and stability conditions with reference to the Hankel transform of the radial profiles and describing some fundamental mathematical properties. Finally some applications are illustrated through examples.

Cumulant Series Expansion of Hybrid Nonlinear Moments of /et

We will now present a simple example to illustrate the approach. Assume four receiver elements at (0, 0, 0), (1, 0, 0). (0, 1, 0), and (0, 0. 1) and a target at (2, 0, 0). By direct computation, we find 6rl = I, 6r2 = 2 - & and 6ri = 2 - &, Given that 6r, = I, 6r2 = 6ri = 2 - h, and that receivers are located at (0, 0, 0), (I, 0, 0), (0, I, 0). and (0, 0, I), we will compute the coordinates of the target.

Bussgang-zero crossing equalization: an integrated HOS-SOS approach

An integrated higher order statistics (HOS) and second order statistics (SOS) based equalization technique is presented as an extension of the Bussgang equalization algorithm. This extension allows one to simultaneously take account of the statistical knowledge about the data source, as done in the conventional HOS approaches and, in particular, by Bussgang-like equalization algorithms such as super exponential, constant modulus, etc., and the spectral redundancy usually present in pulse-amplitude modulation (PAM) and quadrature-amplitude modulation (QAM) modulated signals, exploited by SOS-based approaches. The technique presented employs a new form of SOS equalization that naturally integrates into the Bussgang scheme. It is based on a zero crossing (ZC) property of the received signal when it is passed through a suitable filter. The novel equalization scheme is presented in a Bayesian estimation framework, after illustration of the general Bussgang paradigm and of the principles of the ZC approach. From simulated experiments, results show that the extended Bussgang-ZC equalizer not only outperforms conventional Bussgang equalizers but is also robust to situations where HOS and SOS approaches individually fail.

Bandpass nonlinear systems identification by higher order cross correlation

Nonlinear systems constituted by a zero-memory nonlinearity cascaded with linear filters can be identified by input-output cross correlation using a Gaussian input signal. The method is extended to complex systems through a pair of complex invariance theorems. The stated properties allow identifying the linear parts of systems characterized by magnitude/phase nonlinearities with the joint use of second- and third-order input-output moments. The method can be employed for a wide class of communication bandpass circuits when signals are represented by complex envelopes. >