Ramdas Kumaresan

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.

An algorithm for pole-zero modeling and spectral analysis

An explicit connection between fitting exponential models and pole-zero models to observed data is made. The fitting problem is formulated as a constrained nonlinear minimization problem. This problem is then solved using a simplified iterative algorithm. The algorithm is applied to simulated data, and the performance of the algorithm is compared to previous results.

Data adaptive signal estimation by singular value decomposition of a data matrix

A new method is presented for estimating the signal component of a noisy record of data. Only a little prior information about the signal is assumed. Specifically, the approximate value of rank of a matrix which is formed from the samples of the signal is assumed to be known or obtainable from singular value decomposition (SVD).

Fast base extension using a redundant modulus in RNS

A technique to extend the base of a residue number system (RNS) based on the Chinese remainder theorem (CRT) and the use of a redundant modulus, is proposed. The technique obtains the residue(s) of a given number in the extended moduli without resorting to the traditional mixed-radix conversion (MRC) algorithm. The base extension can be achieved in log/sub 2/n table lookup cycles, where n is the number of moduli in the RNS. The superiority of the technique, compared in terms of latency and hardware requirements to the traditional Szabo-Tanaka method is demonstrated. >

A Prony method for noisy data: Choosing the signal components and selecting the order in exponential signal models

Pronys method is a simple procedure for determining the values of parameters of a linear combination of exponential functions. Until recently, even the modern variants of this method have performed poorly in the presence of noise. We have discovered improvements to Pronys method which are based on low-rank approximations to data matrices or estimated correlation matrices [6]-[8], [15]-[27], [34]. Here we present a different, often simpler procedure for estimation of the signal parameters in the presence of noise. This procedure has received only limited dissemination [35]. It is very close in form and assumptions to Pronys method. However, in preliminary tests, the performance of the method is close to that of the best available, more complicated, approaches which are based on maximum likelihood or on the use of eigenvector or singular value decompositions.

Model-based approach to envelope and positive instantaneous frequency estimation of signals with speech applications

An analytic signal s(t) is modeled over a T second duration by a pole-zero model by considering its periodic extensions. This type of representation is analogous to that used in discrete-time systems theory, where the periodic frequency response of a system is characterized by a finite number of poles and zeros in the z-plane. Except, in this case, the poles and zeros are located in the complex-time plane. Using this signal model, expressions are derived for the envelope, phase, and the instantaneous frequency of the signal s(t). In the special case of an analytic signal having poles and zeros in reciprocal complex conjugate locations about the unit circle in the complex-time plane, it is shown that their instantaneous frequency (IF) is always positive. This result paves the way for representing signals by positive envelopes and positive IF (PIF). An algorithm is proposed for decomposing an analytic signal into two analytic signals, one completely characterized by its envelope and the other having a posit...

On decomposing speech into modulated components

We model a segment of filtered speech signal as a product of elementary signals as opposed to a sum of sinusoidal signals. Using this model, one can better appreciate the basic relationships between envelopes and phases or instantaneous frequencies (IFs) of signals. These relationships reveal some interesting properties of the signals modulations. For instance, if the contribution due to a signals envelope, specifically the Hilbert transform of its log-envelope, is removed from the signals phase, then the resulting signals IF is strictly positive. In addition, filtered speech signal having a bandwidth of B Hz can be essentially represented by the log-envelope and IF that have the same B Hz bandwidths. We extend the above ideas to decompose speech into modulated components. Specifically, a bank of data-adaptive filters (in a cross-coupled configuration) are used to decompose speech into its components; each adaptive filter is a simple single resonance bandpass filter (whose center-frequency or pole-location closely follows the desired formant frequency) supplemented by an adaptive all-zero filter (whose zero-locations sufficiently reduce unwanted leakage from neighboring formants). The filtered components are then represented by their respective log-envelopes and positive IFs; these small number of modulations closely approximate the speech signal.

Improved spectral resolution II

We present more information about improved methods for estimation of the frequencies of sinusoids which are closely spaced in frequency and which are observed in the presence of noise using limited apertures in time and/or space. We compare our realization of maximum likelihood estimation of multiple frequencies with an improved version of Owsleys method and with the forward-backward prediction method advocated by Ulrych and Clayton and by Marple.

A two-dimensional technique for frequency-wavenumber estimation

Simultaneous frequency and wavenumber estimation using two-dimensional (2-D) linear prediction on a space-time data array is investigated. The method used is a direct extension of our previously presented one-dimensional (1-D) frequency estimation technique. It is relatively simple computationally and is superior to the 2-D Fourier transform method in resolving signals closely spaced in frequency and wavenumber.

Data-adaptive principal component signal processing

Principal component (eigenvalue-eigenvector) analysis is applied to processing of narrow band signals in noise. The amount of data available is assumed to be limited. Principal eigenvalues and eigenvectors of a sample correlation matrix are used to improve the signal to noise ratio (SNR) in the data and to increase the resolution capability of nonlinear least squares at low SNR and linear prediction based frequency estimation methods. Relation to Pronylike methods is explored. Performance of different methods is compared experimentally among themselves and to the Cramer-Rao (CR) bound.