Related papers: Multiuser Communication Based on the DFT Eigenstru…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite…
In this letter, we study multiuser communication systems enabled by an unmanned aerial vehicle (UAV) that is equipped with a directional antenna of adjustable beamwidth. We propose a fly-hover-and-communicate protocol where the ground…
With the increasing demand for multi-carrier communication in high-mobility scenarios, it is urgent to design new multi-carrier communication waveforms that can resist large delay-Doppler spreads. Various multi-carrier waveforms in the…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
The fast Fourier transform (FFT) is a primitive kernel in numerous fields of science and engineering. OpenFFT is an open-source parallel package for 3-D FFTs, built on a communication-optimal domain decomposition method for achieving…
This paper investigates dynamic hybrid beamforming (HBF) for a dual-function radar-communication (DFRC) system, where the DFRC base station (BS) simultaneously serves multiple single-antenna users and senses a target in the presence of…
How could the Fourier and other transforms be naturally discovered if one didn't know how to postulate them? In the case of the Discrete Fourier Transform (DFT), we show how it arises naturally out of analysis of circulant matrices. In…
We report experimental implementation of discrete Fourier transformation(DFT) on a nuclear magnetic resonance(NMR) quantum computer. Experimental results agree with theoretical results. Using the pulse sequences we introduced, DFT can be…
A novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical…
We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Lo\`eve transform, and several others along with their continuous counterparts (Fourier transform, Fourier series,…
Eigenvectors of the discrete Fourier transform can be expressed using Ramanujan theta functions. New theta function identities, Ramanujan theta function identities, and generating functions for the quadratic numbers are a consequence.
As a promising technology in beyond-5G (B5G) and 6G, dual-function radar-communication (DFRC) aims to ensure both radar sensing and communication on a single integrated platform with unified signaling schemes. To achieve accurate sensing…
We propose to employ a multilevel detection (MLDT) technique to allow multiple users which respectively transmit messages over independent fading channels to share the same resource, e.g., the same signature sequence in the CDMA (code…
Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each…
Affine Frequency Division Multiplexing (AFDM), a new chirp-based multicarrier waveform for high mobility communications, is introduced here. AFDM is based on discrete affine Fourier transform (DAFT), a generalization of discrete Fourier…
Digital filters for recursively computing the discrete Fourier transform (DFT) and estimating the frequency spectrum of sampled signals are examined, with an emphasis on magnitude-response and numerical stability. In this tutorial-style…
Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…
New services and applications are causing an exponential increase in internet traffic. In a few years, current fiber optic communication system infrastructure will not be able to meet this demand because fiber nonlinearity dramatically…
Beamspace processing is an emerging technique to reduce baseband complexity in massive multiuser (MU) multiple-input multiple-output (MIMO) communication systems operating at millimeter-wave (mmWave) and terahertz frequencies. The high…