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.

iMUSIC: A Family of MUSIC-Like Algorithms for Integer Period Estimation

Abstract: The MUSIC algorithm is one of the most popular techniques today for line spectral estimation. If the line spectrum is that of a periodic signal, can we adapt MUSIC to exploit the additional harmonicity in the spectrum? Important prior work in this direction includes the Harmonic MUSIC algorithm and its variations. For applications where the period of the discrete signal is an integer (or can be well approximated by an integer), this paper introduces a new and simpler class of alternatives to MUSIC. This new family, called iMUSIC, also includes techniques where simple integer valued vectors are used in place of complex exponentials for both representing the signal subspace, and for computing the pseudo-spectrum. It will be shown that the proposed methods not only make the computations much simpler than prior periodicity-adaptations of MUSIC, but also offer significantly better estimation accuracies for applications with integer periods. These advantages are demonstrated on examples that include repeats in protein and DNA sequences. The iMUSIC algorithms are based on the recently proposed Ramanujan subspaces and nested periodic subspaces. The resulting signal space bases are non-Vandermonde in structure. Consequently, many aspects of classical MUSIC that were based on the Vandermonde structure of complex-exponentials, such as guarantees for identifiability of the frequencies (periods in our case), are addressed in new ways in this paper.

Spectral Analysis of Natural Seismic Events Using Autoregressive Techniques

Abstract: This paper presents results illustrating the use of high-resolution spectral estimation methods in the analysis of natural seismic events produced by a small earthquake. The methods used are based on autoregressive (AR) data modelling, originally introduced by Burg as maximum-entropy spectral analysis. In addition, a recently proposed adaptive AR method is also examined. Comparisons with conventionally generated power spectra show that the higher resolution spectra computed using the AR technique provide additional useful information for these data. The adaptive AR results indicate that the signatures may be characterized by the early arrival of a high-frequency component near 0.009 Hz which decays to a value of 0.007 Hz at 25 s after onset.

A Subspace Approach to Spectral Quantification for MR Spectroscopic Imaging

Abstract: Objective: To provide a new approach to spectral quantification for magnetic resonance spectroscopic imaging (MRSI), incorporating both spatial and spectral priors. Methods: A novel signal model is proposed, which represents the spectral distributions of each molecule as a subspace and the entire spectrum as a union of subspaces. Based on this model, the spectral quantification can be solved in two steps: 1) subspace estimation based on the empirical distributions of the spectral parameters estimated using spectral priors; and 2) parameter estimation for the union-of-subspaces model incorporating spatial priors. Results: The proposed method has been evaluated using both simulated and experimental data, producing impressive results. Conclusion: The proposed union-of-subspaces representation of spatiospectral functions provides an effective computational framework for solving the MRSI spectral quantification problem with spatiospectral constraints. Significance: The proposed approach transforms how the MRSI spectral quantification problem is solved and enables efficient and effective use of spatiospectral priors to improve parameter estimation. The resulting algorithm is expected to be useful for a wide range of quantitative metabolic imaging studies using MRSI.

Derivation of discrete Fourier transform components of a time dependent signal

Abstract: An automatic equalizer for calculating the equalization transfer function and applying same to equalize received signals. The initial calculation as well as the equalization proper are conducted entirely within the frequency domain. Overlapping moving window samplings are employed together with the discrete Fourier transformation and a sparse inverse discrete Fourier transformation to provide the equalized time domain output signals.

Discrete evolutionary transform for time-frequency analysis

Abstract: We propose a new transformation for discrete signals with time-varying spectra. The kernel of this transformation provides the energy density of the signal in time-frequency. With this discrete evolutionary transform we obtain a representation for the signal as well as its time-frequency energy density. To obtain the kernel of the transformation we use either the Gabor or the Malvar discrete signal representations. Signal adaptive analysis can be done using modulated or chirped bases, and implemented with either masking or image segmentation on the time-frequency plane. Different examples illustrate the implementation of the discrete evolutionary transform.