Spectral density estimation

About: Spectral density estimation is a research topic. Over the lifetime, 5391 publications have been published within this topic receiving 123105 citations.

Discrete simulation of colored noise and stochastic processes and 1/f/sup /spl alpha// power law noise generation

Abstract: This paper discusses techniques for generating digital sequences of noise which simulate processes with certain known properties or describing equations. Part I of the paper presents a review of stochastic processes and spectral estimation (with some new results) and a tutorial on simulating continuous noise processes with a known autospectral density or autocorrelation function. In defining these techniques for computer generating sequences, it also defines the necessary accuracy criteria. These methods are compared to some of the common techniques for noise generation and the problems, or advantages, of each are discussed. Finally, Part I presents results on simulating stochastic differential equations. A Runge-Kutta (RK) method is presented for numerically solving these equations. Part II of the paper discusses power law, or 1/f/sup /spl alpha//, noises. Such noise processes occur frequently in nature and, in many cases, with nonintegral values for /spl alpha/. A review of 1/f noises in devices and systems is followed by a discussion of the most common continuous 1/f noise models. The paper then presents a new digital model for power law noises. This model allows for very accurate and efficient computer generation of 1/f/sup /spl alpha// noises for any /spl alpha/. Many of the statistical properties of this model are discussed and compared to the previous continuous models. Lastly, a number of approximate techniques for generating power law noises are presented for rapid or real time simulation. >

Time-dependent ARMA modeling of nonstationary signals

Abstract: Modeling of nonstationary signals can be achieved through time-dependent autoregressive moving-average models and lattices, by the use of a limited series expansion of the time-varying coefficients in the models. This method leads to an extension of several well-known techniques of stationary spectral estimation to the nonstationary case. Time-varying AR models are identified by means of a fast (Levinson) algorithm which is also suitable for the AR part of a mixed ARMA model. An alternative to this method is given by the extension of Cadzow's method. Lattices with time-dependent reflection coefficients are identified through an algorithm which is similar to Burg's. Finally, the Prony-Pisarenko estimator is adapted to this nonstationary context, the signal considered in this case being the output of a zero-input time-varying system corrupted by an additive white noise. In all these methods the estimation is global in the sense that the parameters are estimated over a time interval [0, T], given the observations [y 0 ... y T ]. The maximum likelihood method which falls within the same framework is also briefly studied in this paper. Simulations of these algorithms on chirp signals and on transitions between phonemes in speech conclude the paper.

ESPRIT-estimation of signal parameters via rotational invariance techniques

Abstract: High-resolution signal parameter estimation is a problem of significance in many signal processing applications. Such applications indude direction-of-arrival estimation, system identification, and time series analysis. A novel approach to the general problem of signal parameter estimation is described. Although discussed in the context of directionof- arrival estimation, ESPRIT can be applied to a wide variety of problems. It exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure. The technique, when applicable, manifests significant performance and computational advantages over previous algorithms such as Burg's maximum entropy method, Capon's maximum likelihood method, and Schmidt's multiple signal classification.

Interpolation Algorithms for Discrete Fourier Transforms of Weighted Signals

Abstract: A new scheme is presented for the determination of the parameters that characterize a multifrequency signal. The essential innovation is that the signal is weighted before the discrete Fourier transform (DFT) is calculated from which the frequencies and complex amplitudes of the various components of the signal are obtained by interpolation. It is shown that by using the Hanning window for tapering substantial improvements are achieved in the following respects: i) more accurate results are obtained for interpolated frequencies, etc., ii) harmonic interference is much less troublesome even if many tones with comparable strengths are present in the spectrum, iii) nonperiodic signals can be handled without an a priori knowledge of the tone frequencies. The stability of the new method with respect to noise and arithmetic roundoff errors is carefully examined.