Short-time Fourier transform: Two fundamental properties and an optimal implementation

Shift and rotation invariance properties of linear time-frequency representations are investigated. It is shown that among all linear time-frequency representations, only the short-time Fourier transform (STFT) family with the Hermite-Gaussian kernels satisfies both the shift invariance and rotation invariance properties that are satisfied by the Wigner distribution (WD). By extending the time-bandwidth product (TBP) concept to fractional Fourier domains, a generalized time-bandwidth product (GTBP) is defined. For mono-component signals, it is shown that GTBP provides a rotation independent measure of compactness. Similar to the TBP optimal STFT, the GTBP optimal STFT that causes the least amount of increase in the GTBP of the signal is obtained. Finally, a linear canonical decomposition of the obtained GTBP optimal STFT analysis is presented to identify its relation to the rotationally invariant STFT

Generalized time-bandwidth product optimal short-time fourier transformation

By extending the time-bandwidth product concept to fractional Fourier domains, a generalized time-bandwidth product (GTBP) is introduced. The GTBP provides a rotation independent measure for the support of the signals in time-frequency domain. A close form expression for the adaptive kernel of STFT that provides the minimum increase on the GTBP of a signal is derived. Also, a linear canonical decomposition of the obtained GTBP optimal STFT is presented to identify its relation to the rotationally invariant STFT analysis

Dynamic and Sparsity Adaptive Compressed Sensing Based Active User Detection and Channel Estimation of Uplink Grant-Free SCMA

In uplink (UL) grant-free sparse code multiple access (SCMA) systems, unlike the conventional contention-based transmission, users' activities should be known before data decoding due to sporadic transmission in massive machine-type communication (mMTC). Since compressed sensing (CS) is the theory of sparse signal reconstruction with fewer samples, this theory is a good solution to detect active users. In this paper, we propose the dynamic and sparsity adaptive compressed sensing (DSACS) based active user detection (AUD) and channel estimation (CE) of UL grant-free SCMA. Unlike most of the CS-based methods, sparsity knowledge or potential active user list is not needed in the proposed algorithm, which is already not known in the practical systems. The proposed algorithm adopts a stagewise approach to expand the set of accurate active users for adaptively achieve the sparsity level. It uses the temporal correlation of users' activity to improve performance and reduce complexity. Then, false detected users are eliminated with joint message passing algorithm (JMPA), and channel gains of the accurate active users are estimated again in CE with feedback. The simulation results show that the proposed method without sparsity knowledge is capable of achieving detection in various scenarios in case of sporadic transmission in mMTC

A novel STFT implementation for the analysis of non-stationary jammer interference

A novel adaptive short-time Fourier transform (STFT) implementation for the analysis of non-stationary multi-component jammer signals is introduced. The proposed time-frequency distribution is the fusion of optimum STFTs of individual signal components that are based on the recently introduced generalized time-bandwidth product (GTBP) definition. The GTBP optimal STFTs of the components are combined through thresholding and obtaining the individual component support images, which are related with the corresponding GTBP optimal STFTs

High resolution time-frequency analysis by fractional domain warping

A new algorithm is proposed to obtain very high resolution time-frequency analysis of signal components with curved time-frequency supports. The proposed algorithm is based on fractional Fourier domain warping concept introduced in this work. By integrating this warping concept to the recently developed directionally smoothed Wigner distribution algorithm [1], the high performance of that algorithm on linear, chirp-like components is extended to signal components with curved time-frequency supports. The main advantage of the algorithm is its ability to suppress not only the cross-cross terms, but also the auto-cross terms in the Wigner distribution. For a signal with N samples duration, the computational complexity of the algorithm is O(N log N) flops for each computed slice of the new time-frequency distribution

Efficient computation of joint fractional Fourier domain signal representation

A joint fractional domain signal representation is proposed based on an intuitive understanding from a time-frequency distribution of signals that designates the joint time and frequency energy content. The joint fractional signal representation (JFSR) of a signal is so designed that its projections onto the defining joint fractional Fourier domains give the modulus square of the fractional Fourier transform of the signal at the corresponding orders. We derive properties of the JFSR, including its relations to quadratic time-frequency representations and fractional Fourier transformations, which include the oblique projections of the JFSR. We present a fast algorithm to compute radial slices of the JFSR and the results are shown for various signals at different fractionally ordered domains. © 2008 Optical Society of America

Generalization of time-frequency signal representations to joint fractional Fourier domains

The 2-D signal representations of variables rather than time and frequency have been proposed based on either Hermitian or unitary operators. As an alternative to the theoretical derivations based on operators, we propose a joint fractional domain signal representation (JFSR) based on an intuitive understanding from a time-frequency distribution constructing a 2-D function which designates the joint time and frequency content of signals. The JFSR of a signal is so designed that its projections on to the defining joint fractional Fourier domains give the modulus square of the fractional Fourier transform of the signal at the corresponding orders. We derive properties of the JFSR including its relations to quadratic time-frequency representations and fractional Fourier transformations. We present a fast algorithm to compute radial slices of the JFSR

Relativistic K shell decay rates and fluorescence yields for Zn, Cd and Hg

In this work we use the multiconfiguration Dirac-Fock method to calculate the transition probabilities for all possible decay channels, radiative and radiationless, of a K shell vacancy in Zn, Cd and Hg atoms. The obtained transition probabilities are then used to calculate the corresponding fluorescence yields which are compared to existing theoretical, semi-empirical and experimental results

Quantifying methane point sources from fine-scale satellite observations of atmospheric methane plumes

Anthropogenic methane emissions originate from a large number of relatively small point sources. The planned GHGSat satellite fleet aims to quantify emissions from individual point sources by measuring methane column plumes over selected ∼ 10×10&thinsp;km2 domains with  ≤ 50×50&thinsp;m2 pixel resolution and 1&thinsp;%–5&thinsp;% measurement precision. Here we develop algorithms for retrieving point source rates from such measurements. We simulate a large ensemble of instantaneous methane column plumes at 50×50&thinsp;m2 pixel resolution for a range of atmospheric conditions using the Weather Research and Forecasting model (WRF) in large eddy simulation (LES) mode and adding instrument noise. We show that standard methods to infer source rates by Gaussian plume inversion or source pixel mass balance are prone to large errors because the turbulence cannot be properly parameterized on the small scale of instantaneous methane plumes. The integrated mass enhancement (IME) method, which relates total plume mass to source rate, and the cross-sectional flux method, which infers source rate from fluxes across plume transects, are better adapted to the problem. We show that the IME method with local measurements of the 10&thinsp;m wind speed can infer source rates with an error of 0.07–0.17&thinsp;t&thinsp;h−1 + 5&thinsp;%–12&thinsp;% depending on instrument precision (1&thinsp;%–5&thinsp;%). The cross-sectional flux method has slightly larger errors (0.07–0.26&thinsp;t&thinsp;h−1 + 8&thinsp;%–12&thinsp;%) but a simpler physical basis. For comparison, point sources larger than 0.3&thinsp;t&thinsp;h−1 contribute more than 75&thinsp;% of methane emissions reported to the US Greenhouse Gas Reporting Program. Additional error applies if local wind speed measurements are not available and may dominate the overall error at low wind speeds. Low winds are beneficial for source detection but detrimental for source quantification.</p

Relationships within aphids Cinara (Cupressobium) (Hemiptera) based on mitochondrial and nuclear DNA sequences

The relationships between Cinara (Cupressobium) aphids inhabiting woody parts and leaves of conifers belonging to Cupressaceae have been studied using a mitochondrial gene (COI) and a nuclear gene (EF1-α). Based on the COI sequences, genetic distances between species ranged from 5.6 % between Cinara (C.) tujafilina (del Guercio) and Cinara (C.) juniperi (De Geer) to 10.5 % between C. (C.) tujafilina and Cinara (C.) mordvilkoi (Pašek). Genetic distances among EF1-α sequences were lower and showed from 0.1 % between C. cupressi and C. juniperi to 2.3 % between C. tujafilina and C. mordvilkoi. Molecular phylogenetic trees were constructed using the Bayesian inference (BI) phylogenetic analysis and maximum parsimony (MP) criterion. Phylogenetic trees obtained based on COI and EF1-α marker genes created two sister clades. Our results indicate that Cinara (Cupressobium) are a monophyletic group of aphids. Phylogenetic relationships amongst Cupressobium aphids do not result from the association with the host plant, but from the feeding site on the host plant or an ability to change the microhabitat on the plant. As closely related species inhabit similar microhabitats on different host plants, it suggests that the host switching is the main mode of speciation in this subgenus