Fast Fourier Transform
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Related Articles from SNS
On the Role of the Double Fourier Sphere Method in Fast Algorithms on SO(3)
arXiv:2602.06677v3 Announce Type: replace Abstract: We analyze the Double Fourier Sphere (DFS) method on the rotation group $\mathcal{SO}(3)$ in the frequency domain and demonstrate its central role in fast algorithms. Fast Fourier algorithms on $\mathcal{SO}(3)$ are commonly formulated as a Wigner transform - mapping harmonic to Fourier coefficients - followed by a Fourier transform. We revisit this formulation and interpret the Wigner transform as an explicit realization of the DFS method,...
MOSAIC: A Workload-Driven Simulation and Design-Space Exploration Framework for Heterogeneous NPUs
Announce Type: new Abstract: AI model architectures are diversifying rapidly. Although dense matrix multiplication underlies today's CNNs and transformers, emerging architectures (state-space models, long convolutions via the fast Fourier transform (FFT), Kolmogorov-Arnold networks, and spiking networks) are not multiply-accumulate (MAC) dominated; they spend much of their computation on vector and non-MAC primitives that homogeneous, MAC-centric neural processing units (NPUs) serve poorly....
MOSAIC: A Workload-Driven Simulation and Design-Space Exploration Framework for Heterogeneous NPUs
arXiv:2606.05362v2 Announce Type: replace Abstract: AI model architectures are diversifying rapidly. Although dense matrix multiplication underlies today's CNNs and transformers, emerging architectures (state-space models, long convolutions via the fast Fourier transform (FFT), Kolmogorov-Arnold networks, and spiking networks) are not multiply-accumulate (MAC) dominated; they spend much of their computation on vector and non-MAC primitives that homogeneous, MAC-centric neural processing...
Resonant Method-based Fully Automated Core Loss Measurement System for Sub-MHz Magnetics With Switched Capacitor Sequence
Announce Type: new Abstract: Accurate loss characterization is essential for the design of high-frequency power magnetic components. State-of-the-art resonant characterization methods are attractive for high accuracy and low sensitivity, especially at the MHz regime. However, they predominantly rely on manual tuning and computationally intensive Fast Fourier Transform (FFT) analysis to identify resonant conditions, causing both inefficiencies and inaccuracies.
Non-periodic Fourier propagation algorithms for partial differential equations
arXiv:2507.21757v2 Announce Type: replace Abstract: Spectral methods for partial differential equations (PDEs) with non-periodic boundary conditions arising in computational physics often use polynomial expansions on non-uniform grids. Here, we implement a Fourier method that employs fast trigonometric expansions on a uniform grid with non-periodic boundaries using fast discrete sine transforms (DST) or/and discrete cosine transforms (DCT) to solve parabolic PDEs. We implement this method in...
Fourier Neural Operators with rank-1 lattice points and hyperbolic cross
Announce Type: new Abstract: The \emph{Fourier neural operator} (FNO) is a neural network architecture that learns mappings between function spaces. Its efficient implementation is based on the multi-dimensional Fourier transform. By deriving general regularity bounds for the FNO with respect to both the spatial and parametric variables, we prove that the generalization error of the FNO can be improved by replacing spatial tensor product grids with purpose-built rank-1 lattice points, and by...
Global Plane Waves From Local Gaussians: Periodic Charge Densities in a Blink
arXiv:2601.19966v2 Announce Type: replace-cross Abstract: We introduce ELECTRAFI, a fast, end-to-end differentiable model for predicting periodic charge densities in crystalline materials. ELECTRAFI constructs anisotropic Gaussians in real space and exploits their closed-form Fourier transforms to analytically evaluate plane-wave coefficients via the Poisson summation formula. This formulation delegates non-local and periodic behavior to analytic transforms, enabling reconstruction of the...
Global Plane Waves From Local Gaussians: Periodic Charge Densities in a Blink
arXiv:2601.19966v2 Announce Type: replace-cross Abstract: We introduce ELECTRAFI, a fast, end-to-end differentiable model for predicting periodic charge densities in crystalline materials. ELECTRAFI constructs anisotropic Gaussians in real space and exploits their closed-form Fourier transforms to analytically evaluate plane-wave coefficients via the Poisson summation formula. This formulation delegates non-local and periodic behavior to analytic transforms, enabling reconstruction of the...
Feds unwittingly leak pilots' pre-crash conversation
The US National Transportation Safety Board (NTSB) released a spectrographic image derived from the cockpit audio of a UPS plane crash, despite a policy against releasing such recordings. Technically skilled individuals were able to reconstruct approximate audio from the image, prompting the NTSB to acknowledge the privacy breach. The board stated that federal law prohibits the public release of sensitive cockpit communications.
Fast spectral separation method for kinetic equation with anisotropic non-stationary collision operator retaining micro-model fidelity
arXiv:2510.15093v2 Announce Type: replace Abstract: We present a generalized, data-driven collisional operator for one-component plasmas, learned from molecular dynamics simulations, to extend the collisional kinetic model beyond the weakly coupled regime. The proposed operator features an anisotropic, non-stationary collision kernel that accounts for particle correlations typically neglected in classical Landau formulations. To enable efficient numerical evaluation, we develop a fast...