The wavelet transform, time-frequency localization and signal analysis
1990/01/01 by Ingrid Daubechies, I. Daubechies · 89 citations
Computer Science · Engineering · #Image and Signal Denoising Methods #Blind Source Separation Techniques #Machine Fault Diagnosis Techniques
paper · doi:10.1109/18.57199
Abstract
Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied. The first procedure is the short-time or windowed Fourier transform; the second is the wavelet transform, in which high-frequency components are studied with sharper time resolution than low-frequency components. The similarities and the differences between these two methods are discussed. For both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time-frequency density. Finally, the notion of time-frequency localization is made precise, within this framework, by two localization theorems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Citations
Cited by
- Sampling theorems for shift-invariant spaces, Gabor frames, and totally positive functions
- Gabor frames for rational functions
- Some Weyl-Heisenberg frame bound calculations
- Pattern formation outside of equilibrium
- Continuous and Discrete Wavelet Transforms
- The 𝑎𝑏𝑐-problem for Gabor systems
- WAVELET TRANSFORMS AND THEIR APPLICATIONS TO TURBULENCE
- Gabor orthogonal bases and convexity
- A Hybrid Precipitation Prediction Method based on Multicellular Gene Expression Programming
- Modified Frame Reconstruction Algorithm for Compressive Sensing
- Direct Band-Energy Estimation from Finite Samples via Continuous Slepian Multitapers
- Phase Structure in Rotary Attention: A Spectral Framework for Semantic Continuity and Execution-Boundary Governance
- Sparse Operator-Adapted Wavelet Decomposition Using Polygonal Elements for Multiscale FEM Problems
- Data-Efficient Learning of Anomalous Diffusion with Wavelet Representations: Enabling Direct Learning from Experimental Trajectories
- The vibrations of thin plates
- (p,q)-frames in shift-invariant subspaces of mixed Lebesgue spaces Lp,q(R× Rd)
- Effective Series Decomposition and Components Learning for Time Series Generation
- A Hilbert C*-module for Gabor systems
- The abc-problem for Gabor systems
- Multidimensional wavelet frames
- The dual-tree complex wavelet transform
- Time–frequency signal processing: Today and future
- Universal approach to overcoming nonstationarity, unsteadiness and non-Markovity of stochastic processes in complex systems
- On the invertibility of "rectangular" bi-infinite matrices and\n applications in time--frequency analysis
- Time-Frequency Partitions and Characterizations of Modulation Spaces with Localization Opertors
- Simulation of groundwater level variations using wavelet combined with neural network, linear regression and support vector machine
- Recognising realistic emotions and affect in speech: State of the art and lessons learnt from the first challenge
- On Wilson bases in L2(Rd)
- Matching pursuits with time-frequency dictionaries
- Localization of the complex spectrum: the S transform
- Adversarial Attacks with Time-Scale Representations
- Mother wavelet functions generalized through<i>q</i>-exponentials
- Model-free measure of coupling from embedding principle
- Representations of coherent and squeezed states in a<i>f</i>-deformed Fock space
- RINS-T: Robust Implicit Neural Solvers for Time Series Linear Inverse Problems
- GAN-based image steganography by exploiting transform domain knowledge with deep networks
- From Weyl-Heisenberg Frames to Infinite Quadratic Forms
- Analyzing the Weyl-Heisenberg Frame Identity
- Gaussian networks for direct adaptive control
- Exploration of Pattern-Matching Techniques for Lossy Compression on Cosmology Simulation Data Sets
- Image Processing Tools for Financial Time Series Classification
- Unveiling What Makes Saturn Ring: Quantifying the Amplitudes of Saturn's Planetary Normal‐Mode Oscillations and Trends in C‐Ring Properties Using Kronoseismology (VII)
- Universal Scalable Robust Solvers from Computational Information Games\n and fast eigenspace adapted Multiresolution Analysis
- Complex-Valued Symbol Transmissions in Filter Bank Multicarrier Systems using Filter Deconvolution
- Characterization of atomic decompositions, Banach frames, Xd-frames, duals and synthesis-pseudo-duals, with application to Hilbert frame theory
- Face Image Analysis using AAM, Gabor, LBP and WD features for Gender, Age, Expression and Ethnicity Classification
- A New Parameter Estimation Algorithm Based on Sub-band Dual Frequency Conjugate LVT
- Efficient Image Encryption and Decryption Using Discrete Wavelet\n Transform and Fractional Fourier Transform
- Multi-level Wavelet Convolutional Neural Networks
- Learning Object-Centric Representations in SAR Images with Multi-Level Feature Fusion
- Weaving Information Packets
- Recall Gabor Communication Theory and Joint Time-Frequency Analysis
- Fast 2-D Complex Gabor Filter with Kernel Decomposition
- Noise Homogenization via Multi-Channel Wavelet Filtering for High-Fidelity Sample Generation in GANs
- Interpretable Super-Resolution via a Learned Time-Series Representation
- An Introduction to Silent Paralinguistics
- Characteristics of solar diurnal variations: a case study based on records from the ground magnetic observatory at Vassouras, Brazil
- Continuous frames in Krein spaces
- UrbanRhythm: Revealing Urban Dynamics Hidden in Mobility Data
- Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
- Remarks on multivariate Gaussian Gabor frames
- Hierarchical Finite-Element Analysis of Multiscale Electromagnetic Problems via Sparse Operator-Adapted Wavelet Decomposition
- Machine learning in geo- and environmental sciences: From small to large scale
- Detection of Paroxysmal Atrial Fibrillation using Attention-based\n Bidirectional Recurrent Neural Networks
- Gabor representations of evolution operators
- Multifocal ERG wavelet packet decomposition applied to glaucoma diagnosis. [europepmc]
- Time-frequency analysis of band-limited EEG with BMFLC and Kalman filter for BCI applications. [europepmc]
- Cosinor-based rhythmometry. [europepmc]
- Decoding the ERD/ERS: influence of afferent input induced by a leg assistive robot. [europepmc]
- Neural substrates of view-invariant object recognition developed without experiencing rotations of the objects. [europepmc]
- Computer aided-diagnosis of prostate cancer on multiparametric MRI: a technical review of current research. [europepmc]
- EEG Single-Trial Detection of Gait Speed Changes during Treadmill Walk. [europepmc]
- Comparison of Matching Pursuit Algorithm with Other Signal Processing Techniques for Computation of the Time-Frequency Power Spectrum of Brain Signals. [europepmc]
- Evaluation of Early-Age Concrete Compressive Strength with Ultrasonic Sensors. [europepmc]
- Activations of deep convolutional neural networks are aligned with gamma band activity of human visual cortex. [europepmc]
- An Improved Deep Forest Model for Predicting Self-Interacting Proteins From Protein Sequence Using Wavelet Transformation. [europepmc]
- Evaluation of Aboveground Nitrogen Content of Winter Wheat Using Digital Imagery of Unmanned Aerial Vehicles. [europepmc]
- Comparison of Bagging and Boosting Ensemble Machine Learning Methods for Automated EMG Signal Classification. [europepmc]
- DeepFHR: intelligent prediction of fetal Acidemia using fetal heart rate signals based on convolutional neural network. [europepmc]
- An interactive ImageJ plugin for semi-automated image denoising in electron microscopy. [europepmc]
- Time-Resolved Vibrational Analysis of Excited State Ab Initio Molecular Dynamics to Understand Photorelaxation: The Case of the Pyranine Photoacid in Aqueous Solution. [europepmc]
- A Review of Early Fault Diagnosis Approaches and Their Applications in Rotating Machinery. [europepmc]
- A Comprehensive Fault Diagnosis Method for Rolling Bearings Based on Refined Composite Multiscale Dispersion Entropy and Fast Ensemble Empirical Mode Decomposition. [europepmc]
- Automatic ECG Classification Using Continuous Wavelet Transform and Convolutional Neural Network. [europepmc]
- LungINFseg: Segmenting COVID-19 Infected Regions in Lung CT Images Based on a Receptive-Field-Aware Deep Learning Framework. [europepmc]
- Wavelet Analysis of Overnight Airflow to Detect Obstructive Sleep Apnea in Children. [europepmc]
- Water-Mediated Excited State Proton Transfer of Pyranine-Acetate in Aqueous Solution: Vibrational Fingerprints from Ab Initio Molecular Dynamics. [europepmc]
- Non-linear Methods Predominant in Fetal Heart Rate Analysis: A Systematic Review. [europepmc]
- A deep learning mixed-data type approach for the classification of FHR signals. [europepmc]
- Artificial Intelligence-Based Robust Hybrid Algorithm Design and Implementation for Real-Time Detection of Plant Diseases in Agricultural Environments. [europepmc]
Related