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.

Spectral density estimation for random fields via periodic embeddings

Abstract: We introduce methods for estimating the spectral density of a random field on a [Formula: see text]-dimensional lattice from incomplete gridded data. Data are iteratively imputed onto an expanded lattice according to a model with a periodic covariance function. The imputations are convenient computationally, in that circulant embedding and preconditioned conjugate gradient methods can produce imputations in [Formula: see text] time and [Formula: see text] memory. However, these so-called periodic imputations are motivated mainly by their ability to produce accurate spectral density estimates. In addition, we introduce a parametric filtering method that is designed to reduce periodogram smoothing bias. The paper contains theoretical results on properties of the imputed-data periodogram and numerical and simulation studies comparing the performance of the proposed methods to existing approaches in a number of scenarios. We present an application to a gridded satellite surface temperature dataset with missing values.

Quasidistributions, tomography, and fractional Fourier transform in signal analysis

Abstract: The quasidistribution functions like the Ville-Wigner function, the Husimi-Kano function, and the coherent-state approach of Glauber and Sudarshan are reviewed in their application to signal analysis and information processing. Noncommutative tomography of an analytic signal and its relation to the fractional Fourier transform is discussed. The analogy of the analytic signal and the quantum wave function is used to show the identity of the fractional Fourier transform and the Green function of the harmonic oscillator. The approach is discussed for both time-dependent signals and spatial signals.

One-Bit compressive sampling with time-varying thresholds for multiple sinusoids

Abstract: Wide-band spectral sensing is a challenging task that will be required in future cognitive radio and radar applications. Recent research has shown that sampling using only one-bit of amplitude precision can be realized at an extremely high rate [1] in an affordable manner. In this work, one-bit sampling using time-varying thresholds is considered for line spectral estimation. The time-varying thresholds allow for amplitude estimation. A novel one-bit RELAX algorithm is developed for multi-tone parameter estimation. This algorithm is shown to have excellent performance via a numerical example.

Inverse Discrete Fourier Transform-Discrete Fourier Transform Techniques for Generating and Receiving Spectrally Efficient Frequency Division Multiplexing Signals

Abstract: Problem statement: Spectrally Efficient Frequency Division Multiplexing (SEFDM) system promises bandwidth savings by multiplexing overlapped non-orthogonal sub-carriers. However, the loss of orthogonality results in increasing the complexity of generation and detection of the signal. In this work, we propose simple framework for the generation of the SEFDM signal based on the Inverse Discrete Fourier Transform (IDFT). Approach: This study further proposes the use of the Discrete Fourier Transform (DFT) as the receiver front end, specifically for extracting the statistics of the signal needed for recovering the transmitted signal. The proposed transmitter designs employ similar building blocks as Orthogonal Frequency Division Multiplexing (OFDM) based systems, hence, would facilitate an easy migration and/or coexistence with OFDMon the transmitter side. Furthermore, the proposed framework may facilitate the IDFT design for any Frequency Division Multiplexed (FDM) signal with arbitrary sub-carriers spacing. Results and Conclusion: The equivalence of the IDFT generated signal and the modulators based signal is proved mathematically, nonetheless, numerical simulations were performed to verify that equivalence and to test for the performance of the digitally generated signal in AWGN channel. Numerical results confirmed the required spectrum compression and Bit Error Rate (BER) performance at a much reduced complexity.

The key role of tapering in spectrum estimation

Abstract: A number of advantages of employing a taper (or data window) prior to computing the Fourier transform of an observed stretch of time series are reviewed.