Time-Frequency Warped Waveforms

The forthcoming communication systems are advancing towards improved flexibility in various aspects. Improved flexibility is crucial to cater diverse service requirements. This letter proposes a novel waveform design scheme that exploits axis warping to enable peaceful coexistence of different pulse shapes. A warping transform manipulates the lattice samples non-uniformly and provides flexibility to handle the time-frequency occupancy of a signal. The proposed approach enables the utilization of flexible pulse shapes in a quasi-orthogonal manner and increases the spectral efficiency. In addition, the rectangular resource block structure, which assists an efficient resource allocation, is preserved with the warped waveform design as well.Comment: 4 pages, 5 figures; accepted version (The URL for the final version: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8540914&isnumber=8605392

Optical Phase-Space-Time-Frequency Tomography

We present a new approach for constructing optical phase-space-time-frequency tomography (OPSTFT) of an optical wave field. This tomography can be measured by using a novel four-window optical imaging system based on two local oscillator fields balanced heterodyne detection. The OPSTFT is a Wigner distribution function of two independent Fourier Transform pairs, i.e., phase-space and time-frequency. From its theoretical and experimental aspects, it can provide information of position, momentum, time and frequency of a spatial light field with precision beyond the uncertainty principle. We simulate the OPSTFT for a light field obscured by a wire and a single-line absorption filter. We believe that the four-window system can provide spatial and temporal properties of a wave field for quantum image processing and biophotonics.Comment: 11 pages, 6 figure

Audio Classification from Time-Frequency Texture

Time-frequency representations of audio signals often resemble texture images. This paper derives a simple audio classification algorithm based on treating sound spectrograms as texture images. The algorithm is inspired by an earlier visual classification scheme particularly efficient at classifying textures. While solely based on time-frequency texture features, the algorithm achieves surprisingly good performance in musical instrument classification experiments

Time-Frequency Transfer with Quantum Fields

Clock synchronisation relies on time-frequency transfer procedures which involve quantum fields. We use the conformal symmetry of such fields to define as quantum operators the time and frequency exchanged in transfer procedures and to describe their transformation under transformations to inertial or accelerated frames. We show that the classical laws of relativity are changed when brought in the framework of quantum theory.Comment: 4 page

Regular Representations of Time-Frequency Groups

In this paper, we study the Plancherel measure of a class of non-connected nilpotent groups which is of special interest in Gabor theory. Let $G$ be a time-frequency group. More precisely, that is $G=\left\langle T_{k},M_{l}:k\in\mathbb{Z}^{d},l\in B\mathbb{Z}^{d}\right\rangle ,$ $T_{k}$, $M_{l}$ are translations and modulations operators acting in $L^{2}(\mathbb{R}^{d}),$ and $B$ is a non-singular matrix. We compute the Plancherel measure of the left regular representation of $G\$which is denoted by $L.$ The action of $G$ on $L^{2}(\mathbb{R}^{d})$ induces a representation which we call a Gabor representation. Motivated by the admissibility of this representation, we compute the decomposition of $L$ into direct integral of irreducible representations by providing a precise description of the unitary dual and its Plancherel measure. As a result, we generalize Hartmut F\"uhr's results which are only obtained for the restricted case where $d=1$, $B=1/L,L\in\mathbb{Z}$ and $L>1.$ Even in the case where $G$ is not type I, we are able to obtain a decomposition of the left regular representation of $G$ into a direct integral decomposition of irreducible representations when $d=1$. Some interesting applications to Gabor theory are given as well. For example, when $B$ is an integral matrix, we are able to obtain a direct integral decomposition of the Gabor representation of $G.