This letter is the first part of a three-part tutorial on orthogonal time frequency space (OTFS) modulation, which promising candidate waveform for future wireless networks. introduces and compares two popular implementations OTFS namely symplectic finite Fourier transform (SFFT)- discrete Zak (DZT)-based architectures. Based these transceiver architectures, fundamental concepts including delay...

Message passing (MP) aided detectors are designed for orthogonal time frequency space (OTFS) modulated system. We first characterize the transmit-receive relationship of our OTFS-modulated system in delay-Doppler (DD) domain by designing a joint factor graph. Based on this graph, we then conceive message (JMPA) detector. Furthermore, novel low-complexity Gaussian approximate MP (GA-MP) detector...

In this paper, we investigate the impacts of transmitter and receiver windows on performance orthogonal time-frequency space (OTFS) modulation propose window designs to improve OTFS channel estimation data detection performance. particular, assuming ideal pulse shaping filters at transceiver, derive windowing effective its in delay-Doppler (DD) domain, total average transmit power, noise covari...

Observing the dynamics of compact astrophysical objects provides insights into their inner workings, thereby probing physics under extreme conditions. The immediate vicinity an active supermassive black hole with its event horizon, photon ring, accretion disk, and relativistic jets is a perfect place to study general relativity magneto-hydrodynamics. observations M87* Very Long Baseline Interfe...

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The Synchrosqueezing transform is a time-frequency analysis method that can decompose complex signals into time-varying oscillatory components. It is a form of time-frequency reassignment that is both sparse and invertible, allowing for the recovery of the signal. This article presents an overview of the theory and stability properties of Synchrosqueezing, as well as applications of the techniq...

The analysis of historical or ethnical musical instruments can provide means to verify and broaden our knowledge on musical acoustics. The Turkish tanbur, a member of evidently the oldest group of lute instruments, is a good example. Some important features of the instrument include its body resonator (a wooden hemispherical shell covered with a shallow plate) without a sound hole, its violin-l...

Future design procedures for civil structures, especially those to be protected from extreme and blast related loads, will need to account for temporal evolution of their frequency content. Separate time analysis and frequency analysis by themselves do not fully describe the nature of these nonstationary dynamic loads. In the past few years, significant effort has been devoted to wavelets and t...

We develop a theory of almost periodic elements in Banach algebras and present an abstract version of a noncommutative Wiener’s Lemma. The theory can be used, for example, to derive some of the recently obtained results in time-frequency analysis such as the spectral properties of the finite linear combinations of time-frequency shifts.