Frequencies Of Multiple Sinusoids Research Articles

Sparse Robust Learning From Flipped Bits

In wireless sensor networks (WSNs), distributed sensors are often constrained by their limited battery energy and radio spectrum for transmission. This paper investigates an on-line parameter estimation problem of linear regression in a WSN, where each sensor is restricted to send a one-bit message $+1/-1$ to a fusion center in order to satisfy the spectrum and power constraints. Moreover, sensor nodes communicate with the fusion center over noisy links, which can randomly flip the binary message sent from each sensor to the fusion center. With the flipped bit stream, robust and sparse-robust learning algorithms respectively are proposed. In the proposed algorithms, the parameter estimation over a WSN with the imperfect binary communication is formulated hierarchically as Bayesian learning, and is equivalent to an expectation maximization realized by using the recursive least-squares methods. Theoretical and empirical research is carried out to assess the performance of the proposed algorithms, and a practical application of the proposed algorithms in estimation and tracking of frequencies of multiple sinusoids is also presented. These theoretical analysis and experimental results demonstrate the effectiveness of the proposed algorithms.

Subspace Alignment and Separation for Multiple Frequency Estimation

In this letter, a new subspace based estimator that can effectively provide the order and frequencies of multiple sinusoids in noise is proposed. The estimator, referred to as SAS-Est (Subspace Aligning and Separating Estimator), simultaneously seeks to separate the steering vectors from the noise subspace and align them to the signal subspace. The angles between subspaces and the generalized Kullback-Leibler divergence are used in characterizing the alignment and separation. Minimizing the divergence leads to maximal subspace separation and best alignment, thus allowing improved performance. Simulations in additive white Gaussian noise show that the new estimator offers an improvement for both model order and frequency estimation. When compared with other methods, the improvement is more pronounced for high model orders and low signal-to-noise ratio values.

Feasibility of breast cancer lesion detection using a multi-frequency trans-admittance scanner (TAS) with 10 Hz to 500 kHz bandwidth

We describe a new multi-frequency technique for breast cancer detection. Applying a constant voltage with multiple sinusoidal frequencies between a reference electrode on a distal part of a patient and a scan probe placed on the breast, we measure exit currents from an array of electrodes inside the probe that are kept at the ground potential. The distribution of measured exit currents is called the trans-admittance map and the instrument is called the trans-admittance scanner (TAS). We assume a three-dimensional homogeneous domain including an internal lesion with a complex conductivity different from that of the background. Mathematically analyzing the multi-frequency trans-admittance map obtained on the surface of the domain, we found that both conductivity and permittivity ratios between the background and the lesion are crucial in extracting any useful information about the lesion from the map. Choosing two frequencies in the range of 10 Hz to 500 kHz with one significantly lower than the other and assuming that conductivity values of the background and the lesion do not change much from the low to high frequency, the lesion underneath the probe can be detected only when the conductivity ratio between the background and the lesion is different from the permittivity ratio between the background and the lesion at the chosen high frequency. Results of numerical simulations and saline phantom experiments using a developed TAS system are well matched with the mathematical analysis. The biggest advantage of this multi-frequency technique is that we do not need separately measured reference data in the absence of any lesion. We suggest future studies of a more sophisticated lesion detection algorithm based on the analysis and findings described in this paper.

On Simultaneous Estimation of the Number of Signals and Frequencies of Multiple Sinusoids When Some Observations Are Missing

In an earlier article (Bai et al., 1999), the problem of simultaneous estimation of the number of signals and frequencies of multiple sinusoids is considered in the case that some observations are missing. The number of signals is estimated with an information theoretic criterion and the frequencies are estimated with eigenvariation linear prediction. Asymptotic properties of the procedure are investigated but the Monte Carlo simulation is not performed. In this article, a slightly different but scale invariant criterion for detection is proposed and the estimation of frequencies remains the same. Asymptotic properties of this new procedure are provided. Monte Carlo Simulation for both procedures is carried out. Furthermore, comparison on the real signals is also given.

Asymptotic analysis of a fast algorithm for efficient multiple frequency estimation

Based on an asymptotic analysis of the contraction mapping (CM) method of Li and Kedem (1993), a bandwidth shrinkage rule is proposed for fast and accurate estimation of the frequencies of multiple sinusoids from noisy measurements. The CM frequency estimates are defined as the fixed points of a contractive mapping formed by the lag-one autocorrelation coefficient calculated from the output. of a parametric filter applied to the observed time series. With bandwidth parameters judiciously chosen according to the asymptotic analysis, the algorithm is shown to be able to accommodate possibly poor initial values of precision O(n/sup -1/3/) and converge to a final estimate whose accuracy is arbitrarily close to O(n/sup -3/2/), the optimal error rate for frequency estimation under the Gaussian assumption. The total computational complexity of the algorithm is shown to be O(n log n), which is comparable to that of n-point fast Fourier transform (FFT). A novelty in the asymptotic analysis is that it accommodates closely spaced frequencies by allowing not only the filter bandwidth but also the frequency separation to be functions of the sample size n. This enables an assessment of the accuracy of the frequency estimates for given bandwidths and initial values in situations where some or all of the frequencies are close to each other.

The simultaneous estimation of the number of signals and frequencies of multiple sinusoids when some observations are missing: I. Asymptotics.

The problem of simultaneous estimation of the number of signals and frequencies of multiple sinusoids is considered in the case when some observations are missing. The number of signals is estimated with an information theoretic criterion, and the frequencies are estimated with eigenvariation linear prediction. The strong consistency of the estimates of the number of signals and the frequencies is established and the rate of convergence of these estimates is provided. Besides, the limiting distributions of various estimates are given.

MATRIX PENCIL METHODS FOR 2-D FREQUENCY ESTIMATION

The problem of estimating two-dimensional frequencies of multiple sinusoids embedded in noise is addressed. A variant of the recently reported matrix pencil method is proposed. Numerical results that provide insights into the perturbation deviations of the estimated two-dimensional frequencies are given for both methods. The variant method is shown to be computationally much more efficient than the original method while their accuracies are comparable.

Linear estimation of frequencies of multiple sinusoids with least-absolute error criterion

The estimation problem of sine wave frequencies is investigated. The forward-backward linear prediction method (FBLP1) with least-absolute error criterion is used to improve the frequency estimate performance attained by the linear prediction method (FBLP2) with the least-square error criterion. Theoretical and computer simulations show that the FBLP1 method has performances similar and superior to the FBLP2 method.

Perturbation analysis of an SVD-based linear prediction method for estimating the frequencies of multiple sinusoids

A linear prediction approach is studied for estimating the frequencies of sinusoids in white noise. It is shown that in the first step, the continuity of the generalized inverse and the concept of angle between subspaces play an important role. The continuity concept helps explain the need for a low rank approximation, and the quality of the approximation is appraised by using the notion of angle between subspaces. For the second step, the sensitivity of the zeros of the predictor polynomial becomes an important consideration and is examined. It is shown that increasing the order of the predictor polynomial and computing the minimum norm solution provides a mechanism to reduce parameter sensitivity. >