New method extracts fetal ECG from maternal abdominal ECG.
problem Extract fetal ECG from single-lead maternal abdominal ECG.
method De-shape short time Fourier transform for heart rate estimation, beat tracking, and nonlocal median for waveform reconstruction.
result The method accurately extracts fetal ECG signals from maternal abdominal ECG signals.
The paper proposes using CWT and STFT for training neural speech models.
problem Training high-quality neural speech models.
method Proposes spectral amplitude and phase losses from STFT and CWT for training.
result Shows that CWT spectral loss can train a high-quality model as good as STFT-based loss.
Proposes a differentiable STFT for more efficient optimization of hop length.
problem Efficient optimization of hop length in STFT for better temporal control.
method Introduces a differentiable version of STFT with continuous hop length.
result Improves optimization methods like gradient descent for STFT.
Proposes AWS method for precise speech enhancement using DNN.
problem T-F resolution problem in fixed-resolution short-time frequency transforms.
method Incorporates trainable adaptive window switching into speech enhancement procedure.
result Achieved higher signal-to-distortion ratio than conventional methods.
Efficient trainable front-end for neural speech enhancement.
problem Inefficient STFT front-ends in neural speech enhancement models.
method Butterfly mechanism for Fast Fourier Transform, trainable STFT window.
result Accuracy and efficiency improvements for low-compute systems.
Generative model improves audio synthesis from TF features.
problem Challenges in generating high-quality audio from TF features.
method Used a GAN to generate invertible TF features from short-time Fourier transforms.
result Generated TF features from GAN outperformed direct waveform generation.
Combines Fourier methods and RNNs for efficient time series prediction.
problem Efficiently processing and predicting time series data with memory and computational constraints.
method Uses short-time Fourier transform and weight reductions through low pass filtering in a Spectral RNN.
result Predicts time series data from chaotic systems and real-world data.
STFNets learn signals from time-frequency perspective, outperforming traditional models.
problem Learning signals from IoT data with better features in the frequency domain.
method Integrates Short-Time Fourier Transform into neural networks for direct frequency domain feature learning.
result Significantly outperforms state-of-the-art models in various experiments.
The Fourier transform of Heegaard Floer d-invariants helps classify 3-manifolds.
problem Classifying 3-manifolds up to integer homology cobordism.
method Exploring the Fourier transform of Heegaard Floer d-invariants.
result Lens spaces are cancellable in the monoid of 3-manifolds up to integer homology cobordism.
A new method integrates Fourier basis expansion and mapping for improved time series forecasting.
problem Inconsistent starting cycles and series length issues in Fourier-based methods.
method Fourier Basis Mapping (FBM) method that integrates time-frequency features through Fourier basis expansion and mapping.
result FBM addresses inconsistencies and preserves temporal characteristics, achieving SOTA performance.
The study proves fractional-order differences and equations are key to modeling long and short memory in economics.
problem Modeling long and short memory in economic processes with discrete fractional differencing and integration.
method Proved discrete fractional differencing and integration are Grunwald-Letnikov fractional differences of non-integer order d. ARIMA and ARFIMA models are fractional-order difference equations. Proved exact fractional-order differences are needed for power law memory.
result Fractional differential equations are necessary for modeling continuous time long and short memory with power law.
Improved speech emotion recognition using pitch-synchronous single frequency filtering spectrogram.
problem Uncertainty principles in STFT spectrogram limit time and frequency resolutions.
method Modified SFF spectrogram by averaging amplitudes between GCI locations, named pitch-synchronous SFF spectrogram.
result Improved SER accuracy (63.95% to 70.4%) on IEMOCAP dataset.
Novel ECG classification method using deep time-frequency representation and progressive decision fusion.
problem Challenges in classifying abnormal ECG rhythms due to broad taxonomy, noises, and lack of annotated data.
method Transform ECG signal into time-frequency domain, train scale-specific deep CNNs, and fuse decisions progressively.
result Effective and efficient ECG classification method validated on synthetic and real-world datasets.
Novel neural network layer improves long-range interactions in point clouds.
problem Efficiently treating long-range interactions in point clouds.
method Long-range convolutional (LRC)-layer that incorporates Fourier transforms.
result Global all-to-all convolution operation performed in nearly-linear time.
A new quasi-Newton method tackles NMF with transform learning on orthogonal manifolds.
problem Efficiently learning transforms for NMF in non-convex optimization on orthogonal manifolds.
method Derives a quasi-Newton method on the orthogonal matrix manifold using sparse approximations of the Hessian.
result Outperforms state-of-the-art methods by orders of magnitude in experiments on synthetic and real audio data.
Paper proves Fourier transform for valuations, simplifying previous work.
problem Existence of isomorphism for translation-invariant smooth valuations.
method Directly describes Alesker's isomorphism in terms of Fourier transform on functions.
result Simple proofs of Alesker's Fourier transform properties, including a previously conjectured result.
Adversarial attacks on spectrograms can fool audio classifiers trained on waveforms.
problem Susceptibility of audio classifiers to adversarial attacks on spectrograms.
method Applying adversarial attacks to spectrograms and reconstructing audio waveforms.
result Perturbed spectrograms can fool 2D CNNs and 1D CNNs trained on audio waveforms.
TSLANet improves time series models by capturing long-term and short-term interactions.
problem Noise sensitivity, computational efficiency, and overfitting in Transformer-based models for time series data.
method Adaptive Spectral Block and Interactive Convolution Block for robust feature representation and noise mitigation.
result TSLANet outperforms state-of-the-art models in various time series tasks.
A new algorithm computes Fourier coefficients for a specified range efficiently.
problem Inefficiency in FFT due to fixed output size for all applications.
method Fast Partial Fourier Transform (PFT) that allows specifying the range of Fourier coefficients to compute.
result PFT achieves significant speedup over state-of-the-art FFT algorithms for small output sizes.
ConvNet classifies whale vocalizations and ambient noise in acoustic recordings.
problem Automated detection and classification of marine mammal vocalizations in acoustic recordings.
method Convolutional Neural Network with a novel acoustic representation.
result Classifier accurately detects and classifies whale vocalizations and ambient noise.
Deep neural networks improve speech steganography for covert messaging.
problem Improving steganography for speech data using deep learning.
method Proposed a new deep neural network model with short-time Fourier transform layers, demonstrating effectiveness on multiple speech datasets.
result Demonstrated that the proposed method can conceal multiple messages in a single carrier and is robust to channel distortions.
Deep neural network estimates support of sparse signals for improved phase retrieval.
problem Sparse phase retrieval from Fourier magnitudes with support estimation.
method Trained deep neural network (DNN) provides extended support estimate E larger than the support T. result DNN-based support estimation improves signal reconstruction performance with lower complexity.
Diffusion models enhance speech without supervision.
problem Challenges in generalizing supervised speech enhancement methods to unseen conditions.
method Unsupervised speech enhancement using diffusion-based generative models.
result Demonstrates promising results compared to supervised and unsupervised baselines.
End-to-end denoising framework improves SDR and PESQ metrics.
problem Spectrum and metric mismatches in speech enhancement networks.
method Optimizes network on time-domain signals after ISTFT and uses improved loss functions.
result Significantly improved SDR and PESQ performance.
iSTFTNet speeds up mel-spectrogram vocoders without sacrificing quality.
problem Efficiently converting mel-spectrograms to speech with minimal computation.
method Replaces convolutional layers with iSTFT after frequency dimension reduction.
result Significant reduction in computational cost with comparable quality.
The paper derives and proves the Helgason Fourier transform for vector bundle-valued differential forms on homogeneous spaces.
problem Deriving the Helgason Fourier transform for vector bundle-valued differential forms on homogeneous spaces.
method Employing the perspective of the functional equation satisfied by the classical Fourier transform, the paper derives the Helgason Fourier transform map and proves its properties.
result The Fourier transform is explicitly given and proven to be a map from vector bundle-valued differential forms to another vector bundle-valued differential form on the product space.
New algorithm for 2D SWDFT reduces redundant calculations.
problem Redundant calculations in overlapping windows for 2D SWDFT.
method Tree data structure based on Cooley-Tukey FFT for efficient computation.
result Our algorithm reduces operations to O(N0N1n0n1). Enhances Fourier estimator performance for asynchronous event-data.
problem Improving correlation and covariance estimation on event-data.
method Implement and test NUFFT methods with different averaging kernels.
result Demonstrates improved performance and relationship between averaging scales.
Acoustic sensors identify vehicles using spectral embedding.
problem Vehicle recognition from roadside audio sensors.
method Extract frequency signatures, apply spectral embedding for dimensionality reduction.
result K-nearest neighbors achieve accurate vehicle identification after dimensionality reduction.
Closed pricing formulas for Variance Gamma model payoffs.
problem Pricing path-independent payoffs in the Variance Gamma model.
method Mellin transform theory and multidimensional complex analysis.
result Closed-form pricing formulas with accelerated convergence for short-term options.
New Fourier transform method handles missing data and asynchronous observations.
problem Volatility inference with missing or asynchronous data.
method Spectral framework using Fourier transforms.
result Consistent volatility functional estimation with limit distributions.
Quantum kernel improves solar irradiance forecasting.
problem Improving short-term solar irradiance forecasting accuracy.
method Quantum Fourier Transform kernel in KRR with feature mixing.
result Consistently improves R2 and nRMSE over classical kernels.
Given two compact hyperkähler surfaces X and Y and a holomorphic vector bundle Q on X×Y, which is a generalized instanton, one can define a Fourier-Mukai transform, which, under suitable assumptions, maps vector bundles on X to vector bundles on Y. If X and Y are dual complex tori, this transform …
New graph Fourier transform distinguishes directions in multi-dimensional signals.
problem Existing graph Fourier transform fails to distinguish directions in multi-dimensional signals.
method Algebraic properties of Cartesian products rearrange 1-D spectra into multi-dimensional frequency domain.
result Solves multi-valuedness of spectra and enables directional frequency analysis.
Simplified derivation and simulation of Feller Diffusion.
problem Deriving the probability density function of Feller Diffusion.
method Fourier Transform and Method of Characteristics for derivation; simulation algorithms for validation.
result Confirmation of hitting time probabilities via simulation.
Sp(n)-instantons linked to complex Lagrangian graphs via Fourier-Mukai transform.
problem Understanding Sp(n)-instantons on hyperkahler manifolds with conical singularities.
method Relating Sp(n)-instantons to deformed instantons and studying their properties on hyperkahler manifolds.
result Sp(n)-instantons on hyperkahler manifolds correspond to tri-contact instantons on the 3-Sasakian link.
Simplified Butterfly-Net2 improves CNN efficiency in solving PDEs and signal processing tasks.
problem Improving CNN efficiency in solving PDEs and signal processing tasks.
method Introducing BNet2, a simplified Butterfly-Net, and Fourier transform initialization.
result BNet2 achieves similar accuracy as CNN but with fewer parameters and improves accuracy over randomly initialized CNN.
We model the price of a stock via a Langévin equation with multi-dimensional fluctuations coupled in the price and in time. We generalize previous models in that we assume that the fluctuations conditioned on the time step are compound Poisson processes with operator stable jump intensities. We derive exact relations f…
Efficiently approximates time series correlation using Fourier transform and neural networks.
problem Efficiently approximating correlation in time series data.
method Embeds time series into a low-dimensional Euclidean space using Fourier transform and neural networks, ensuring accurate correlation approximation from Euclidean distance.
result Our method reduces approximation loss by half and improves top-k correlation search precision from 5% to 20%. Improved numerical solution for BSDEs with reduced boundary errors.
problem Boundary errors in numerical solution of BSDEs.
method Modified damping and shifting schemes to transform target function into a bounded periodic function, applying Fourier transforms.
result Significant reduction in boundary errors with improved accuracy and convergence.
Automatically identifies vehicles from audio sensors without needing labeled data.
problem Vehicle recognition and classification from acoustic signals.
method Incremental reseeding of acoustic signatures using spectral embedding and clustering.
result Incremental reseeding accurately identifies individual vehicles from their acoustic signatures.
In this paper we consider the problem of calculating the quantiles of a risky position, the dynamic of which is described as a continuous time regime-switching jump-diffusion, by using Fourier Transform methods. Furthermore, we study a classical option-based portfolio strategy which minimizes the Value-at-Risk of the h…
Classifies conformally covariant operators between differential forms on spheres.
problem Classifying conformally covariant differential operators between differential forms on spheres.
method F-method based on algebraic Fourier transform of Verma modules, extended to matrix-valued case.
result Explicit formulæ for conformally covariant differential operators in flat coordinates.
We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast F…
Paper computes link determinants using Fourier-Hadamard transforms.
problem Computing determinants of complex link structures.
method Fourier-Hadamard transforms of Boolean functions.
result Determinant of centrally symmetric links with even components equals zero.
NFM models time-series data directly in the Fourier domain, achieving state-of-the-art performance.
problem Traditional time-series analysis focuses on the time domain, limiting flexibility.
method NFM models time-series data in the Fourier domain, using frequency extrapolation and interpolation.
result NFM achieves state-of-the-art performance on various time-series tasks.
Extends option pricing framework without risk-free asset using Levy jumps.
problem Valuing derivatives in markets without a traded risk-free bond.
method Introduces common Levy jump dynamics, uses Ito-Levy calculus, FFT, and COS algorithms.
result Calibrations show jump models reduce pricing errors and fit volatility smiles better than Black-Scholes.
X-ray transform on H-type groups solved, revealing function injectivity.
problem Injectivity in sub-Riemannian geometry.
method Fourier Slice Theorem adapted to H-type groups.
result Integrable functions on H-type groups are uniquely determined by their integrals over geodesics.