Harmonic Retrieval in Colored ARMA Noise

We propose a new approach to harmonic retrieval in colored ARMA noise. A suitable filter is first used to remove all the sharp power spectrum peaks of the noisy observed process, then some kinds of cross correlation is employed to identify the noise characteristics. After filtering the noisy observed process with the identified noise characteristics again, SVD-TLS method can be applied to retrieve the harmonics. The proposed approach can be used to retrieve real-valued harmonic signals in colored ARMA noise with no restrictions on the phase coupling of harmonics and the distribution of the noise. Simulation examples show its effectiveness.

Feasibility of a novel beamforming algorithm via retrieving spatial harmonics

This paper introduces an algorithm for beamforming systems by the aid of multidimensional harmonic retrieval(MHR).This algorithm resolves problems,removes limitations of sampling and provides a more robust beamformer.A new sample space is created that can be used for estimating weights of a new beamforming called spatial-harmonics retrieval beamformer(SHRB).Simulation results show that SHRB has a better performance,accuracy,and applicability and more powerful eigenvalues than conventional beamformers.A simple mathematical proof is provided.By changing the number of harmonics,as a degree of freedom that is missing in conventional beamformers,SHRB can achieve more optimal outputs without increasing the number of spatial or temporal samples.We will demonstrate that SHRB offers an improvement of 4 dB in signal to noise ratio(SNR) in bit error rate(BER) of 10~(-4) over conventional beamformers.In the case of direction of arrival(DOA) estimation,SHRB can estimate the DOA of the desired signal with an SNR of-25 dB,when conventional methods cannot have acceptable response.

Joint eigenvalue estimation by balanced simultaneous Schur decomposition

The problem of joint eigenvalue estimation for the non-defective commuting set of matrices A is addressed. A procedure revealing the joint eigenstructure by simultaneous diagonalization of. A with simultaneous Schur decomposition （SSD） and balance procedure alternately is proposed for performance considerations and also for overcoming the convergence difficulties of previous methods based only on simultaneous Schur form and unitary transformations, it is shown that the SSD procedure can be well incorporated with the balancing algorithm in a pingpong manner, i. e., each optimizes a cost function and at the same time serves as an acceleration procedure for the other. Under mild assumptions, the convergence of the two cost functions alternately optimized, i. e., the norm of A and the norm of the left-lower part of A is proved. Numerical experiments are conducted in a multi-dimensional harmonic retrieval application and suggest that the presented method converges considerably faster than the methods based on only unitary transformation for matrices which are not near to normality.