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.

Time-frequency MUSIC

Abstract: A new method for the estimation of the signal subspace and noise subspace based on time-frequency signal representations is introduced. The proposed approach consists of the joint block-diagonalization (JBD) of a set of spatial time-frequency distribution matrices. Once the signal and noise subspaces are estimated, any subspace based approach, including the multiple signal classification (MUSIC) algorithm, can be applied for direction of arrival (DOA) estimation. Performance of the proposed time-frequency MUSIC (TF-MUSIC) for an impinging chirp signal using three different kernels is numerically evaluated.

A Sampling Theorem For The Complex Spectrogram, And Gabor's Expansion Of A Signal In Gaussian Elementary Signals

Abstract: The complex spectrogram of a signal is defined as the Fourier transform of the product of the signal and the shifted and complex conjugated version of a so-called window function; it is thus a function of time and frequency, simultaneously, from which the signal can be reconstructed uniquely. It is shown that the complex spectrogram is completely determined by its values on the points of a certain time-frequency lattice. This lattice is exactly the one suggested by Gabor in 1946; it arose in connection with Gabor's sugges-tion to expand a signal into a discrete set of Gaussian elementary signals. Such an expansion is a special case of the more general expansion of a signal into a discrete set of properly shifted and modulated window functions. It is shown that this expansion exists. Furthermore, a set of functions is constructed, which is bi-orthonormal to the set of shifted and modulated window functions. With the help of this bi-orthonormal set of functions, the expansion coefficients can be determined easily.

Improved heart rate variability signal analysis from the beat occurrence times according to the IPFM model

Abstract: The heart rate variability (HRV) is an extended tool to analyze the mechanisms controlling the cardiovascular system. In this paper, the integral pulse frequency modulation model (IPFM) is assumed. It generates the beat occurrence times from a modulating signal. This signal is thought to represent the autonomic nervous system action, mostly studied in its frequency components. Different spectral estimation methods try to infer the modulating signal characteristics from the available beat timing on the electrocardiogram signal. These methods estimate the spectrum through the heart period (HP) or the heart rate (HR) signal. The authors introduce a new time domain HRV signal, the Heart Timing (HT) signal. They demonstrate that this HT signal, in contrast with the HR or HP, makes it possible to recover an unbiased estimation of the modulating signal spectra. In this estimation the authors avoid the spurious components and the low-pass filtering effect generated when analyzing HR or HP.

Application of empirical mode decomposition to heart rate variability analysis.

Abstract: The analysis of heart rate variability, involving changes in the autonomic modulation conditions, demands specific capabilities not provided by either parametric or non-parametric spectral estimation methods. Moreover, these methods produce time-averaged power estimates over the entire length of the record. Recently, empirical mode decomposition and the associated Hilbert spectra have been proposed for non-linear and non-stationary time series. The application of these techniques to real and simulated short-term heart rate variability data under stationary and non-stationary conditions is presented. The results demonstrate the ability of empirical mode decomposition to isolate the two main components of one chirp series and three signals simulated by the integral pulse frequency modulation model, and consistently to isolate at least four main components localised in the autonomic bands of 14 real signals under controlled breathing manoeuvres. In addition, within the short time-frequency range that is recognised for heart rate variability phenomena, the Hilbert amplitude component ratio and the instantaneous frequency representation are assessed for their suitability and accuracy in time-tracking changes in amplitude and frequency in the presence of non-stationary and non-linear conditions. The frequency tracking error is found to be less than 0.22% for two simulated signals and one chirp series.

A resolution comparison of several time-frequency representations

Abstract: Two signal components are considered resolved in a time-frequency representation when two distinct peaks can be observed. The time-frequency resolution limit of two Gaussian components, alike except for their time and frequency centers, is determined for the Wigner distribution, the pseudo-Wigner distribution, the smoother Wigner distribution, the squared magnitude of the short-time Fourier transform, and the Choi-Williams distribution. The relative performance of the various distributions depends on the signal. The pseudo-Wigner distribution is best for signals of this class with only one frequency component at any one time, the Choi-Williams distribution is most attractive for signals in which all components have constant frequency content, and the matched filter short-time Fourier transform is best for signal components with significant frequency modulation. A relationship between the short-time Fourier transform and the cross-Wigner distribution is used to argue that, with a properly chosen window, the short-time Fourier transform of the cross-Wigner distribution must provide better signal component separation that the Wigner distribution. >