Ten lectures on wavelets
Time-frequency analysis and synthesis of linear signal spaces: time-frequency filters, signal detection and estimation, and Range-Doppler estimation
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
The hermite transform: a survey
EURASIP Journal on Applied Signal Processing
Accurate image rotation using Hermite expansions
IEEE Transactions on Image Processing
Video frames reconstruction based on time-frequency analysis and Hermite projection method
EURASIP Journal on Advances in Signal Processing - Special issue on time-frequency analysis and its applications to multimedia signals
Time-frequency analysis and hermite projection method applied to swallowing accelerometry signals
EURASIP Journal on Advances in Signal Processing - Special issue on applications of time-frequency signal processing in wireless communications and bioengineering
Multitaper Time-Frequency Reassignment for Nonstationary Spectrum Estimation and Chirp Enhancement
IEEE Transactions on Signal Processing
Blind separation of speech mixtures via time-frequency masking
IEEE Transactions on Signal Processing
The chirplet transform: physical considerations
IEEE Transactions on Signal Processing
Multiple window time-varying spectral analysis
IEEE Transactions on Signal Processing
Hybrid linear/quadratic time-frequency attributes
IEEE Transactions on Signal Processing
Short-time Fourier transform: two fundamental properties and an optimal implementation
IEEE Transactions on Signal Processing
The wavelet transform, time-frequency localization and signal analysis
IEEE Transactions on Information Theory
Time-frequency localization operators: a geometric phase space approach
IEEE Transactions on Information Theory
De-noising by soft-thresholding
IEEE Transactions on Information Theory
Automatic watershed segmentation of randomly textured color images
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Block-Based Neural Networks for Personalized ECG Signal Classification
IEEE Transactions on Neural Networks
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Since Hermite-Gaussian (HG) functions provide an orthonormal basis with the most compact time-frequency supports (TFSs), they are ideally suited for time-frequency component analysis of finite energy signals. For a signal component whose TFS tightly fits into a circular region around the origin, HG function expansion provides optimal representation by using the fewest number of basis functions. However, for signal components whose TFS has a non-circular shape away from the origin, straight forward expansions require excessively large number of HGs resulting to noise fitting. Furthermore, for closely spaced signal components with non-circular TFSs, direct application of HG expansion cannot provide reliable estimates to the individual signal components. To alleviate these problems, by using expectation maximization (EM) iterations, we propose a fully automated pre-processing technique which identifies and transforms TFSs of individual signal components to circular regions centered around the origin so that reliable signal estimates for the signal components can be obtained. The HG expansion order for each signal component is determined by using a robust estimation technique. Then, the estimated components are post-processed to transform their TFSs back to their original positions. The proposed technique can be used to analyze signals with overlapping components as long as the overlapped supports of the components have an area smaller than the effective support of a Gaussian atom which has the smallest time-bandwidth product. It is shown that if the area of the overlap region is larger than this threshold, the components cannot be uniquely identified. Obtained results on the synthetic and real signals demonstrate the effectiveness for the proposed time-frequency analysis technique under severe noise cases.