Study Of Parameter Estimation Of Exponentially Damped Sinusoids And Its Application

Estimation of frequency is an important content of signal processing with growing applications in engineering, such as communication, earthquake, biomedicine, etc. Therefore, estimation of frequency has a very important research value in real application as well as in theory. In recent years, biomedical signal processing becomes an important application of digital signal processing, and it provides a signal model for the research of estimation algorithm of frequency. NMR (Nuclear Magnetic Resonance) signal in biomedical signal analysis can be modeled as a sum of multiple exponentially damped sinusoidal signals, based on this signal model, the main work in this paper can be summarized as follows:Firstly, four classical spectrum estimation algorithms have been introduced: MUSIC algorithm,ESPRIT algorithm,linear prediction algorithm,maximum likelihood algorithm. Then, we present the basic principles and calculation steps of the four methods respectively. The computer simulations are also given to compare the performance of the four methods aforementioned.Secondly, we propose a subspace-based method for joint estimating of the time delay and frequency parameter of multiple exponentially damped sinusoidal signals. The searching computation is not required in the proposed method. Moreover, the proposed approach has better numerical value stability because of being insensitive to the model error. Computer simulations show that the performance of the frequency, damped factor and time delay estimation can attain the CRLB at a wide range of SNR. Finally, the performance of the proposed algorithm is demonstrated via computer simulations using exponentially damped sinusoidal signal as well as real ATP data in medicine engineering.Then, we research a fast method for joint estimating of the time delay and frequency parameter and present an improved propagator method based on LU or QR factorization of the spectral matrix. In the proposed approach, all the signal information is focused in the upper-left triangular matrix, so it improves the robustness to noise. Moreover, the improved method without eigendecomposition has lower computational complexity. Computer simula- tions show that its accuracy is higher than those of the existing methods even when the SNR is low.Lastly, a computationally efficient method that combines the subspace and projection separation approaches is proposed for 3-D frequency estimation of multiple sinusoids. From the perspective that 3-D sinusoids is a series of 2-D sliced matrices distributed in the third dimension, frequency parameters in the first dimension are firstly estimated by employing the conventional MUSIC-based method to the covariance of the series of slice in the third dimension. Subsequently, a set of projection separation matrices is constructed to separate and estimate the frequency parameters in the second and the third dimension through a set of slices distributed in the third and the second dimension, respectively. The estimated frequencies in the second and third dimension are associated with the projection separation matrix derived from frequency in the first dimension, therefore, the 3-D frequency parameters are automatically paired. Simulation results show that the performance of the proposed method is comparable to those of the available IMDF and HOSVD methods.