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

Compilation and review engagements : essential questions and answers

https://egrove.olemiss.edu/aicpa_guides/1524/thumbnail.jp

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

Entanglement demonstration on board a nano-satellite

Global quantum networks for secure communication can be realized using large fleets of satellites distributing entangled photon pairs between ground-based nodes. Because the cost of a satellite depends on its size, the smallest satellites will be most cost-effective. This Letter describes a miniaturized, polarization entangled, photon-pair source operating on board a nano-satellite. The source violates Bell’s inequality with a Clauser–Horne–Shimony–Holt parameter of 2.60±0.06. This source can be combined with optical link technologies to enable future quantum communication nano-satellite missions

SpooQy-1: The First Nano-Satellite to Demonstrate Quantum Entanglement in Space

SpooQy-1 is a 3-unit nanosatellite that was launched into a Low Earth Orbit from the International Space Station on the 17th of June 2019. The spacecraft hosts a scientific payload capable of producing entangled photon-pairs and measuring their polarization in orthogonal bases to perform a Bell test. Since launch, SpooQy-1 has routinely demonstrated the generation and detection of polarization entangled photon-pairs in Space, something that has previously only been demonstrated by the 630kg Micius mission by the Chinese Academy of Sciences. The measured entanglement correlations can violate Bell\u27s inequality with a CHSH parameter value of 2.60±0.06, over operating temperatures of 16 °C to 21.5 °C. These results demonstrate that quantum entanglement can be generated in space on highly resource-constrained platforms. A follow-on 12U mission, developed in partnership with RAL space,will build on this to demonstrate space-to-ground entanglement distribution, which is required for space-based nodes to support global quantum communication networks

Zn treatment effects on biological potential of fennel bulbs as affected by in vitro digestion process

Zn treatment effects on the stability of polyphenols, MDA (malondialdehyde) content, antioxidant and lipoxygenase inhibition activities of two varieties of fennel bulbs were studied by using an in vitro gastrointestinal digestion model. Likewise, the effect of Zn on viability cells of E. coli was also performed. The results revealed that high amounts of total phenolic and flavonoid compounds were released during the digestion process, especially after the intestinal phase. Additionally, the antioxidant and lipoxygenase inhibitory activity were affected by the gastrointestinal digestion process and seems to be correlated with total phenol contents. On the other hand, the viability of E. coli was not affected by the activity of our tested bulbs during passage through the artificial digestion model, but the treated bulbs activity contribute relatively to the inhibition growth of bacteria. The survival of E. coli in fennel bulbs was challenged with simulated gastrointestinal fluids and the results showed that the E. coli strains, despite having experienced a viability reduction at the intestinal phase, were able to overcome the exposure to the gastrointestinal synthetic fluids. This E. coli ability reinforces the need for good hygienic measures to assure safe fresh produce, even for those that are rich in antibacterial compounds.info:eu-repo/semantics/publishedVersio