Harmonic Retrieval Algorithm Research Articles

Fast and accurate estimator for two-dimensional cisoids based on QR decomposition

In this paper, we apply the QR decomposition to parameter estimation for K two-dimensional (2-D) complex-valued sinusoids embedded in additive white Gaussian noise. By exploiting the rank-K and linear prediction (LP) properties of the 2-D noise-free data matrix, we show that the frequencies and damping factors of one dimension can be extracted from the first K rows of R, that is, the upper triangular matrix in the factorization. An iteratively weighted least squares (IWLS) algorithm is then proposed to estimate the LP coefficients from which the sinusoidal parameters in this dimension are computed. The frequencies and damping factors of the remaining dimension are estimated using a similar IWLS procedure such that the 2-D parameters are automatically paired. We thus refer our estimator to as the QR-IWLS algorithm. Moreover, we have analyzed its bias and mean square error performance. In particular, closed-form expressions are derived for the special case of K=1. The performance of the QR-IWLS method is also evaluated by comparing with several state-of-the-art 2-D harmonic retrieval algorithms as well as Cramér–Rao lower bound via computer simulations.

An efficient algorithm for harmonic retrieval by combining blind source separation with wavelet packet decomposition

In the present paper, we propose an efficient framework and algorithm for one dimensional harmonic retrieval problem in additive colored Gaussian or non-Gaussian noise when the frequencies of the harmonic signals are closely spaced in frequency domain. Our framework utilizes the wavelet packet (WP) method to the blind source separation (BSS) based harmonic retrieval model. Firstly, we establish the BSS based harmonic retrieval model in additive noise using only one mixed channel signal, at the same time, the fundamental principle of BSS based harmonics retrieval algorithm is analyzed in detail. Then, the harmonic retrieval algorithm is developed mainly using the WP decomposition approach, where the criterion is formed as the cumulant based approximation of the mutual information (MI) for the selection of optimal sub-bands of WP decomposition with the least-dependent components between the same nodes. Simulation results show that the proposed algorithm is able to retrieve the harmonic source signals and yield good performance.

Tensor-MODE for multi-dimensional harmonic retrieval with coherent sources

We devise a new method of direction estimation (MODE) based multi-dimensional harmonic retrieval algorithm, which is referred to as tensor-MODE (T-MODE). It is a R-dimensional generalization of the conventional MODE and higher-order singular value decomposition is performed on the tensor observations. Asymptotic efficiency is achieved for the proposed estimator even when the source signals are highly correlated or coherent. Furthermore, the computational cost is reasonable, because it consists of polynomial rooting, followed by a combinatorial search, whereas multi-dimensional optimization is not required.

Harmonic retrieval by period blind source extraction method: Model and algorithm

A frequently encountered problem in signal processing field is harmonic retrieval in additive colored Gaussian or non-Gaussian noise, especially when the frequencies of the harmonic signals are closely spaced in frequency domain. The purpose of this paper is to develop novel harmonic retrieval algorithm based on blind source extraction (BSE) method from linear mixtures of harmonic signals using only one observed channel signal. First, we establish the blind source separation (BSS) based harmonic retrieval model in additive noise using the only one observed channel, at the same time, the fundamental principle of BSE based harmonics retrieval algorithm is analyzed in detail. Then, based on the established harmonic BSS model, we propose a BSE approach to the harmonic retrieval using the concept of period BSE method, as a result, the harmonic retrieval algorithm using only one channel mixed signals is derived. Simulation results show that the proposed algorithm is able to separate the harmonic source signals and yield ideal performance.

A Shift Invariance-Based Order-Selection Technique for Exponential Data Modelling

This paper presents a new subspace-based technique for automatic detection of the number of exponentially damped sinusoids. It consists in studying the shift-invariance of the dominant subspace of the Hankel data matrix. No threshold setting and no penalization terms are necessary. This model-based method, easy to implement, can be plugged into most subspace-based harmonic retrieval algorithms.

Blind high-resolution localization and tracking of multiple frequency hopped signals

This paper considers the problem of blind localization and tracking of multiple frequency-hopped spread-spectrum signals using a uniform linear antenna array without knowledge of hopping patterns or directions of arrival. As a preprocessing step, we propose to identify a hop-free subset of data by discarding high-entropy spectral slices from the spectrogram. High-resolution localization is then achieved via either quadrilinear regression of four-way data generated by capitalizing on both spatial and temporal shift invariance or a new maximum likelihood (ML)-based two-dimensional (2-D) harmonic retrieval algorithm. The latter option achieves the best-known model identifiability bound while remaining close to the Cramer-Rao bound even at low signal-to-noise ratios (SNRs). Following beamforming using the recovered directions, a dynamic programming approach is developed for joint ML estimation of signal frequencies and hop instants in single-user tracking. The efficacy of the proposed algorithms is illustrated in pertinent simulations.

Adaptive high-resolution algorithms for tracking nonstationary sources without the estimation of source number

In this paper, a generalized inflation method which can adaptively and robustly converge to the noise-subspace is proposed to improve the performances of subspace algorithms used for tracking nonstationary sources. This generalized inflation method, which includes an inflation factor developed in the view point of orthogonal projection, preserves the parallel structure for realizations and achieves better performances of convergence and initialization behavior than the inflation method, adaptive Pisarenko (1973) harmonic retrieval algorithms, and other adaptive eigensubspace algorithms when the number of sources is not known. A bound of the inflation factor is also suggested to secure the noise-subspace-only adaptation. The general inflation method in use of weighted-subspace can further improve the tracking performances. Simulations for analyzing the tracking performances of the algorithms are also included. >

Improvements of a state-space iterative noise reduction algorithm for harmonic retrieval

When the model of a noisy sinusoidal process is autoregressive moving average (ARMA), then the AR spectrum is biased. However, since the AR spectrum contains all the second-order information of the process, it is possible to retrieve the noiseless predictor from the noisy one. An iterative algorithm enabling the computation of the ARMA parameters from the AR parameters and a new well-suited initialization scheme are presented. Simulations of the state-space iterative noise reduction algorithm (SINA) are performed using various AR estimators. The mean-square-error graph is plotted for all these estimators and performances of the methods are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Harmonic retrieval of analog signals

A harmonic retrieval algorithm, analogous to that of V. Pisarenko (1973), is derived for extracting harmonics from analog data. The analog hardware required consists of integrators and power meters. The power meter outputs are sampled and a Hankel matrix is formed from these quantities. A minimum matrix pencil problem involving this Hankel matrix is then solved to extract the frequency estimates and the power levels of the signal harmonics. >