Identification of rational transfer function from frequencyresponse sample

A method for identifying a transfer function, H(z)=A(z)/B(z), from its frequency response values is presented. Identifying the transfer function involves determining the unknown degrees and coefficients of the polynomials A(z) and B( z), given the frequency response samples. The method for finding the parameters of the transfer function involves solving linear simultaneous equations only. An important aspect of the method is the decoupled manner in which the polynomials A(z) and B(z) are determined. The author presents two slightly different derivations of the linear equations involved, one based on the properties of divided differences and the other using Vandermonde matrices or, equivalently, Lagrange interpolation. A matrix synthesized from the given frequency response samples is shown to have a rank equal to the number of poles in the system     

Estimating the Angles of Arrival of Multiple Plane Waves

The problem of estimating the angles of arrival of M plane waves incident simultaneously on a line array with L + 1 (L?M) sensors utilizing the special eigenstructure of the covariance matrix C of the signal plus noise at the output of the array is addressed. A polynomial D(z) with special properties is constructed from the eigenvectors of C, the zeros of which give estimates of the angle of arrival. Although the procedure turns out to be essentially the same as that developed by Reddi, the development presented here provides insight into the estimation problem.     

Data-Adaptive Detection of a Weak Signal

Motivated by a form of the likelihood-ratio-tesf statistic for detection of a rank-one Gaussian signal in colored Gaussian noise, we apply our earlier technique for estimation of a low-rank signal to the problem of estimating and subtracting the waveform of a strong sinusoidal interference prior to detection of a weak sinusoidal signal. We consider the difficult case in which samples of data are taken over a short interval of time or space and the frequencies of the sinusoidal signal and sinusoidal interference are more closely spaced than the reciprocal of the extent of the aperture. The method can be applied to cases of nonsinusoidal and/or random signals and interference. The most important assumption is that when the samples of the interference are arranged in matrix form the matrix is approximately of low rank in the sense that, with high probability, the interference-only matrix can be well approximated by a matrix of low rank.