Soheil A. Dianat

Adaptive spectral estimation by the conjugate gradient method

This paper proposes an alternative technique for adaptive spectral estimation. The new technique applies the method of conjugate gradient, which is used for iteratively finding the generalized eigenvector corresponding to the minimum generalized eigenvalue of a semidefinite Hermitian matrix, to the adaptive spectral analysis problem. Computer simulations have been performed to compare the new method to existing ones. From the limited examples presented, it is seen that the new method is computationally more efficient at the expense of more core storage. Also, this method is effective for small data records and can implement noise correction to yield unbiased spectral estimates if an estimate of the noise covariance matrix is available. The technique performs well for both narrow-band and wide-band signals.

A novel technique to the solution of transient electromagnetic scattering from thin wires

Previous approaches to the problem of transient scattering by conducting bodies have utilized the well-known marching-on-in-time solution procedures. However, these procedures are very dependent on discretization techniques and in many cases lead to instabilities as time progresses. Moreover, the accuracy of the solution procedure cannot be verified easily and usually there is no error estimation. Recently an alternate approach to the solution of transient scattering by thin wires was presented based on the conjugate gradient (CG) method. In this procedure, space and time are discretized independently into subintervals and the error is minimized iteratively. Unfortunately, this procedure is very slow, not easily extendable to other geometries, and moreover, some of the advantages of marching-on-in-time are lost. In this paper, again the conjugate gradient method is applied to solve the above problem, but this time, reducing the error to a desired value at each time step. Since the error is reduced at each time step, marching-on-in-time can still be done without error accumulation as time progresses. Computationally, this procedure is as fast as conventional marching-on-in-time. Thus, this new method retains all the advantages of marching-on-in-time and yet does not introduce instabilities in the late time. It is also possible to apply this procedure to other geometries. Details of the solution procedure along with numerical results are also presented.

Deconvolution of Impulse Response from Time-Limited Input and Output: Theory and Experiment

Since it is impossible to generate and propagate an impulse, often a system is excited by a narrow time-domain pulse. The output is recorded and then a numerical deconvolution is often done to extract the impulse response of the object. Classically, the fast Fourier transform (FFT) technique has been applied with much success to the above deconvolution problem. However, when the signal-to-noise ratio becomes small, sometimes one encounters instability with the FFT approach. In this paper, the method of conjugate gradient is applied to the deconvolution problem. The problem is solved entirely in the time domain. The method converges for any initial guess in a finite number of steps. Also, for the application of the conjugate gradient method, the time samples need not be uniform, like FFT. Since, in this case, one is solving the operator equation directly, by passing the autocorrelation matrix computation, storage required is 5N as opposed to N2. Computed impulse response utilizing this technique has been presented for measured incident and scattered fields.

Fast algorithms for phase and magnitude reconstruction from bispectra

Techniques are developed for signal reconstruction from sampIes of the bispectrum of a 1-D or 2-D signal. The phase and magnitude of the Fourier transform of a signal as well as those of the bispectrum are expanded into a series using a set of appropriate basis functions. Reconstruction is achieved by equating coefficients of like terms of these two expansions. The algorithms derive their speed by using a restricted portion of the bispectrum space and by being based on the use of the fast Fourier transform. In addition to detailed theoretical derivations, results of computer simulation are provided.

Impulse response determination in the time domain-Theory

Two methods are presented for determining the impulse response of an object in the time domain when both the input and output time domain waveforms are specified. Pole extraction features can then be applied to the nonimpulsive portion of the impulse response to determine the singularity expansion method (SEM) parameters of the object. The first method involves synthetic division and is comparatively straightforward. The second technique is a least squares method which is computationally more stable. The effect of measurement errors in the input and output waveforms is evaluated for each method. An investigation is made as to what form of the input minimizes the noise variances in the computation. Finally a generalized least squares technique is presented, which yields a minimum variance unbiased estimate for the impulse response when the noise covariance matrix is known.

A non-linear predictor for differential pulse-code encoder (DPCM) using artificial neural networks

A nonlinear predictor is designed for a DPCM encoder using artificial neural networks (ANN). The predictor is based on a multilayer perceptron with three input nodes, 30 hidden nodes and one output node. The back-propagation learning algorithm is used for the training of the network. Simulation results are presented to evaluate and compare the performance of the neural net based predictor (nonlinear) with that of an optimized linear predictor. Success in the use of the nonlinear predictor is demonstrated through the reduction in the entropy of the differential error signal as compared to that of a linear predictor. Also it is shown that the ANN predictor is much more robust for encoding noisy images compared to that of a linear predictor.<<ETX>>

Fuzzy system for adaptive network routing

In this paper we propose an adaptive routing using a fuzzy system. The traffic in the network is re-routed to nodes, which are less congested, or have spare capacity. Based on a set of fuzzy rules, link cost is dynamically assigned depending upon the present condition of the network. Distance vector algorithm, which is one of the shortest path routing algorithms is used to build the routing tables at each node in the network. The proposed fuzzy system determines the link cost given the present congestion situation measured via the delays experienced in the network and the offered load on the network. Delay in the links, was estimated by the time taken for the test packets to travel from the node to its neighbors. The delay information collected by the test packets and the number of packets waiting in the queue, are the two inputs to the fuzzy system. The output of the fuzzy system is the link cost. This algorithm was applied on a simulated NSFNET, the USA backbone, as well as to another test network with a different topology. Robustness and optimality of the proposed fuzzy system was tested by simulating various types of load patterns on these networks. Simulation studies showed that the performance of the fuzzy system was very close to or better than the best performance of the composite metric under different load conditions and topologies.

Practical algorithm for the inversion of an experimental input-output color map for color correction

We introduce the iteratively clustered interpolation algorithm to compute a structured printer inverse look-up table from irregularly sampled experimental color data. The algorithm is based on a gradient optimization method, with initial points generated through an iterative technique. Experimental results with a digital color printer are provided to illustrate the algorithm.

Polyspectral factorization: necessary and sufficient condition for finite extent cumulant sequences

The authors provide necessary and sufficient conditions for bispectral and trispectral factorization for processes with finite-extent cumulant sequences. These conditions are derived entirely in terms of the cumulant sequences. They use the fact that for a finite-extent cumulant sequence factorability is equivalent to finding a finite-order moving-average process with an identical cumulant sequence. In principle the results can be extended to polyspectra of even higher orders. An interesting result of the investigation is that there exist processes generated by nonlinear mechanisms that are factorable.<<ETX>>

Differential pulse code modulation image compression using artifical neural networks

Differential pulse code modulation (DPCM) is a widely used technique for both lossy and lossless compression of images. In this paper, the effect of using a nonlinear predictor based on artificial neural networks (ANN) for a DPCM encoder is investigated. The ANN predictor uses a 3-layer perceptron model with 3 input nodes, 30 hidden nodes, and 1 output node. The back-propagation learning algorithm is used for the training of the network. Simulation results are presented to compare the performance of the proposed ANN-based nonlinear predictor with that of a global linear predictor as well as an optimized minimum-mean-squared-error (MMSE) linear predictor. Preliminary computer simulations demonstrate that for a typical test image, the zeroth-order entropy of the differential (error) image can be reduced by more than 15% compared to the case where optimum linear predictors are employed. Some future research directions are also discussed.