Shanglin Ye

An algorithm for the parameter estimation of multiple superimposed exponentials in noise

The parameter estimation of multiple superimposed complex exponentials in noise has been a popular research problem for decades due to its various practical applications. In this paper, we propose a simple yet accurate estimator for estimating the complex amplitudes and frequencies of the superimposed exponentials. Combining an efficient frequency estimator with a leakage subtraction scheme, the novel method iterates to consecutively estimate each component by gradually reducing the estimation error and increasing the estimation accuracy. Simulation results are presented to verify that the proposed algorithm is capable of obtaining estimation performance that is very close to the Cramer-Rao lower bound.

Efficient Iterative Estimation of the Parameters of a Damped Complex Exponential in Noise

The estimation of the frequency and decay factor of a single decaying exponential in noise is a problem of prime importance. A popular estimation scheme uses the computationally efficient implementation of the Discrete Fourier transform, the FFT, to obtain a coarse estimate which is then improved by a fine estimation stage. Such estimators, however, show a performance that degrades and departs from the Cramér-Rao Lower Bound (CRLB) as the number of samples increases. To overcome this problem, we propose an iterative, exponentially windowed algorithm. We derive the new estimators theoretical performance and study its behavior under different decay rates of the window. We show that the estimator has excellent performance that tracks the CRLB with increasing number of samples if the window decay rate is appropriately set.

Rapid accurate frequency estimation of multiple resolved exponentials in noise

The estimation of the frequencies of the sum of multiple resolved exponentials in noise is an important problem due to its application in diverse areas from engineering to chemistry. Yet to date, no low cost Fourier-based algorithm has been successful at obtaining unbiased estimates that achieve the CramrRao lower bound (CRLB) over a wide range of signal-to-noise ratios. In this work, we achieve precisely this goal, proposing a fast yet accurate estimator that combines an iterative frequency-domain interpolation step with a leakage subtraction scheme. By analysing the asymptotic performance and the convergence behaviour of the estimator, we show that the estimate of each frequency converges to the asymptotic fixed point. Thus, the estimator is asymptotically unbiased and the variance is extremely close to the CRLB. We verify the theoretical analysis by extensive simulations, and demonstrate that the proposed algorithm is capable of obtaining more accurate estimates than state-of-the-art high resolution methods while requiring significantly less computational effort. HighlightsAn efficient frequency estimator for multiple resolved complex exponentials in noise is proposed.The proposed estimator is Fourier-based with no singular value decomposition or matrix inversion involved.The variance of the estimates obtained by the proposed method is extremely close to the CramrRao bound.Simulation results show that the proposed estimator can outperform state-of-the-art estimation approaches.

Efficient peak extraction of proton NMR spectroscopy using lineshape adaptation

Nuclear magnetic resonance (NMR) spectroscopy signals are ideally modelled as a superimposition of damped exponentials in additive Gaussian noise. In order to extract the information from these signals, methods are needed to decompose the signal into its components and estimate their parameters. This task can become quite difficult due to factors such as large number of samples, unknown and possibly large number of components, and lineshape distortion. In this paper, we propose a computationally efficient method for peak extraction in proton NMR spectroscopy without any a priori information. This method combines a simple damped complex exponential parameter estimation strategy with lineshape adaptation in the frequency domain. We apply the proposed technique on real NMR data and show that it outperforms competing state of the art methods. It is shown that the new method is capable of extracting very small lines such as satellites.

Two dimensional frequency estimation by interpolation on Fourier coefficients

In this paper, we propose a computationally simple algorithm for the estimation of the frequencies of a random phase two-dimensional (2-D) complex exponential in additive noise by extending the 1-D estimator developed by Aboutanios and Mulgrew. The procedure of the algorithm is based on a two-stage scheme consisting of a coarse estimator followed by a fine search stage. The separability of the problem implies that the estimator can be applied in each direction. Theoretical analysis shows, however, that the performance of the algorithm converges to the minimum point of the asymptotic variance after two iterations only if the estimation is applied jointly in the two dimensions. As in the 1-D case, this variance is extremely close to the 2-D Cramer-Rao Lower Bound. The simulation results are presented to verify the analysis.

A novel algorithm for the estimation of the parameters of a real sinusoid in noise

In this paper, we put forward a computationally efficient algorithm to estimate the frequency and complex amplitude of a real sinusoidal signal in additive Gaussian noise. The novel method extends an iterative frequency estimator for single complex exponentials that is based on interpolation on Fourier coefficients to the real case by incorporating an iterative leakage subtraction strategy. Simulation results are presented to verify that the proposed algorithm can obtain more accurate estimation than both time and frequency domain parameter estimators in the literature, and the estimation variance of the method sits on the Cramer-Rao lower bound with only a few iterations required.

On the Estimation of the Parameters of a Real Sinusoid in Noise

We propose and comprehensively analyze a computationally efficient algorithm to estimate the parameters of a real sinusoidal signal in noise. This method uses the fast Fourier Transform and is, therefore, computationally efficient. Accounting for the interference due to the negative spectral component allows the frequency to be estimated very accurately. Estimates of the amplitude and phase are derived in the process and are necessary for the suppression of the leakage. Theoretical analysis establishes that the estimator is asymptotically unbiased and achieves the Cramér–Rao lower bound. Simulation results are presented to verify the theory and demonstrate that the estimation performance is superior to other estimators in the literature.

Estimating Parameters of Multiple Damped Complex Sinusoids with Model Order Estimation

The estimation of the parameters of damped complex sinusoids is a classic research problem that has been studied extensively. State-of-art high resolution estimators for this problem suffer from certain drawbacks including high computational complexity and the necessity of model order information. In this work, we develop an efficient estimation algorithm to overcome these issues. Specifically, we combine the recently proposed Multi-tone Iterative Windowed A&M (MIWAM) algorithm, a high performance method capable of estimating the frequencies and complex amplitudes of multiple complex sinusoids in white Gaussian noise, with a model order estimation strategy that is based on information theory criteria. We demonstrate through extensive simulations thatthe novel method achieves more reliable performance whilerequiring less computations than high resolution algorithms.

Iterative windowed parameter estimation of multiple superimposed damped exponentials in noise

The research problem of the parameter estimation of multiple superimposed damped complex exponentials in noise is of significant importance in many engineering and science applications. In this paper, we propose a simple yet accurate estimator to address the problem. By combining an efficient windowed frequency and damping estimator for a single component with an iterative leakage subtraction scheme, the novel method consecutively and iteratively estimates one component at a time by gradually reducing the leakage introduced by other components presented. Simulation results are presented to verify that the proposed algorithm is capable of outperforming state-of-art time and frequency domain algorithms.

Efficient 2-D Frequency and Damping Estimation by Interpolation on Fourier Coefficients

This letter focuses on the efficient estimation of the frequencies and damping factors of a single 2-D damped complex exponential in additive Gaussian noise. We derive the estimators by extending the FFT-based frequency estimator that relies on interpolation on Fourier coefficients to 2-D damped signals. Performance analysis shows that the algorithm can achieve minimum variances at the fixed point when implemented in an interleaved manner for two iterations. Furthermore, we propose linearized version of the estimators that render them more amenable to real-time DSP implementation. We also demonstrate that the iterative implementation of the algorithm combining both versions is both unbiased and accurate.