A method is developed to predict the maximum electric and magnetic fields radiated by a printed circuit board (PCB) by measuring the amplitude of magnetic fields very close to the PCB on a planar surface. The vertical component of the magnetic fields in each cell of an imaginary planar grid a few centimetres above the PCB is modelled as due to the magnetic dipole moments situated directly below the measuring point on each cell of another imaginary planar grid on the plane of the PCB. The dipole loops are assumed to be coplanar with the plane of the PCB. Magnetic dipole moments in each cell of the grid are calculated from the magnetic field value measured directly above it. From the dipole moments the amplitude of the electric and magnetic fields can be calculated at any distance from the PCB. To verify the method, two devices were tested: a simple PCB containing a loop with a crystal oscillator and resistor, and a fully populated microprocessor device in its casing. The vertical component of the close magnetic fields are measured using a commercially available close-field magnetic field probe and spectrum analyser. The frequency range from 30 MHz to 110 MHz are covered. The calculated maximum electric field radiation at 3 m from the devices are compared with the directly measured electric field radiation in a semi-anechoic chamber. The calculated and measured values are within 5 dBμV/m of each other for the oscillator circuit and within 9 dBμV/m of each other for the microprocessor device, for each frequency tested

This paper proposes an eigenanalysis-based method for estimating the frequencies of complex-valued sine waves. The basic idea behind this method consists of using a set of linearly independent vectors that are orthogonal to the signal subspace spanned by the principal eigenvectors of the data covariance matrix. Exploiting that orthogonality condition gives an overdetermined system of linear equations, the unknown parameters of which are uniquely related to the frequencies. Analytical expressions are derived for the covariances of the equation errors in the sample version of the aforementioned linear system of equations. Based on these expressions a Markov-like estimate of the unknown parameters is introduced, which asymptotically (with respect to either the number of data samples or the signal-to-noise ratio) provides the minimum variance frequency estimates in a fairly large class of consistent estimators. The paper includes Monte-Carlo simulations that support the theoretical analysis results and show that those results may apply to scenarios with rather low values of the number of data samples and the signal-to-noise ratio. >

The Markov theory for solving perturbed systems of linear equations is applied to the ESPRIT method for direction estimation in array signal processing. The Markov-based ESPRIT estimates of the unknown directions are shown to be significantly more accurate than the commonly used least-squares ESPRIT estimates.

Proposes a class of subspace-based methods for estimating the direction-of-arrival (DOA) of plane waves impinging on an array of sensors. The proposed methods estimate the DOA using only linear operations on the data, and can hence be implemented in a very efficient manner. Furthermore, these methods can accommodate more general noise models than the spatially white noise model commonly used in the literature. Large sample expressions are derived for the variance of the estimates obtained by using the proposed techniques. A comparative statistical study is performed in which comparisons against MUSIC are considered. It is found that usually MUSIC offers slightly more accurate DOA estimates at the cost of an increased computational burden and a more restrictive noise model. The paper includes simulation results lending support to the theoretical results obtained.< >

The authors present expressions for the variance of the multiple signal classification (MUSIC) and ESPRIT frequency estimates derived under the assumption that the sample covariance matrix is close to its asymptotical value. This assumption is valid for a sufficiently high signal-to-noise ratio, but also for a large number of data samples. It is shown that the expressions derived here encompass both the high SNR analysis presented earlier and the large sample analysis described by P. Stoica and T. Soderstrom (IEEE Trans. vol.SP-39, no.8, p.1836-47, Aug. 1991). The theoretical results are supported by the results obtained from Monte Carlo simulations.<>

Expressions are presented for the variance of the MUSIC and ESPRIT estimates of sinusoidal frequencies, for situations when the signal-to-noise ratio (SNR) is high and the number of data is limited. The high SNR variance expressions are compared to the large sample variance expressions presented by Stoica and Soderstrom. The high SNR variance expressions are also valid for reasonable values of the SNR, and should be regarded as a complement to the large sample variance expressions. The theoretical results are supported by Monte Carlo simulations

In a recent paper by Anarim and Istefanopulos, a statistical analysis of the Pisarenko Harmonic Decomposition (PHD) for frequency estimation was carried out. The expression for the variance of the frequency estimate from Anarim and Istefanopulos differs significantly from the expression for the variance of the PHD frequency estimate obtained in earlier studies, e.g. by Sakai, Stoica and Nehorai. In this short communication, we reproduce the analysis from Anarim and Istefanopulos, and obtain an expression for the variance which is identical to the expression derived by Sakai, Stoica and Nehorai.