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Simultaneous Localization and Mapping (SLAM) is an essential technology for the efficiency and reliability of unmanned robotic exploration missions. While the onboard computational capability and communication bandwidth are critically…
High-resolution tissue imaging is often compromised by sample-induced optical aberrations that degrade resolution and contrast. While wavefront sensor-based adaptive optics (AO) can measure these aberrations, such hardware solutions are…
We consider the problem of finding the Discrete Fourier Transform (DFT) of $N-$ length signals with known frequency support of size $k$. When $N$ is a power of 2 and the frequency support is a spectral set, we provide an $O(k \log k)$…
In this work, we introduce a definition of the Discrete Fourier Transform (DFT) on Euclidean lattices in $\R^n$, that generalizes the $n$-th fold DFT of the integer lattice $\Z^n$ to arbitrary lattices. This definition is not applicable for…
Photonic computing has emerged as a promising substrate for accelerating the dense linear-algebra operations at the heart of AI, yet adoption for large Transformer models remains in its infancy. We identify two bottlenecks: (1) costly…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
In this paper, we realize the concept of analog computing using an array of engineered gradient dielectric meta-reflect-array. The proposed configuration consists of individual subwavelength silicon nanobricks in combination with fused…
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…
Modern nanofabrication techniques have enabled us to manipulate the wavefront of light with sub-wavelength-scale structures, offering the potential to replace bulky refractive surfaces in conventional optics with ultrathin metasurfaces. In…
The efficient multiangle centered discrete fractional Fourier transform (MA-CDFRFT) [1] has proven to be a useful tool for time-frequency analysis; in this paper, we generalize the MA-CDFRFT to general M -periodic transforms, which, among…
Rapidly growing demands for high-performance computing, powerful data processing systems, and big data necessitate the advent of novel optical devices to perform demanding computing processes effectively. Due to its unprecedented growth in…
Discrete Fourier transform (DFT) is the base of modern signal or information processing. 1-Dimensional fast Fourier transform (1D FFT) and 2D FFT have time complexity O(NlogN) and O(N^2logN) respectively. Quantum 1D and 2D DFT algorithms…
The perception of autonomous vehicles has to be efficient, robust, and cost-effective. However, cameras are not robust against severe weather conditions, lidar sensors are expensive, and the performance of radar-based perception is still…
Metasurfaces have shown promising potentials in shaping optical wavefronts while remaining compact compared to bulky geometric optics devices. Design of meta-atoms, the fundamental building blocks of metasurfaces, relies on trial-and-error…
In the paper it is shown that there exist infinite classes of fast DFT algorithms having multiplicative complexity lower than O(NlogN), i.e. smaller than their arithmetical complexity. The derivation starts with nesting of Discrete Fourier…
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…
The discrete Fourier transform (DFT) is widely employed for multi-beam digital beamforming. The DFT can be efficiently implemented through the use of fast Fourier transform (FFT) algorithms, thus reducing chip area, power consumption,…
Diffractive Neural Networks (DNNs) leverage the power of light to enhance computational performance in machine learning, offering a pathway to high-speed, low-energy, and large-scale neural information processing. However, most existing DNN…
Flat optics foresees a new era of ultra-compact optical devices, where metasurfaces serve as the foundation. Conventional designs of metasurfaces start with a certain structure as the prototype, followed by an extensive parametric sweep to…
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…