The design of approximate Hilbert transform pairs of wavelet bases

By Ivan W. Selesnick. IEEE Transactions on Signal Processing, 2002

320 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/b8b4ece3f59695af209026719b82839a58669821

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Vision and Pattern Recognition

1. Ivan W. Selesnick
2. Richard Baraniuk
3. Sujit Kumar Bose
4. N. Kingsbury
5. Miguel López-Benítez
6. Fei Ma
7. Enggee Lim
8. Tiantian Guo

In Signal Processing

1. Miguel López-Benítez
2. Fei Ma
3. Enggee Lim
4. Tiantian Guo
5. Tongpo Zhang
6. Limin Yu
7. Richard Baraniuk
8. N. Kingsbury

Citations in the corpus

• Fast Fourier Transform (2011, background): “For a mathematical treatment of the DT CWT see also [115, 103].”
• The double-density dual-tree DWT (2004, methodology): “…we see that must satisfy the following condition: (14) Following the derivation in [25] for orthogonal wavelet bases, we find that for the wavelet frames considered here, if the -periodic functions are defined as (15) and (16) then (14) holds, and therefore, form a Hilbert transform pair for .”
• A Review of Wavelet Analysis and Its Applications: Challenges and Opportunities (2022, methodology): “Selesnick gave the necessary conditions for an orthogonal wavelet system to form a Hilbert transform pair [32] and proposed a construction algorithm based on a delay filter in [33], [34].”
• The dual-tree complex wavelet transform (2005, methodology): “The filters were obtained using the design algorithm in [88] and have two vanishing moments each.”