Introduction to Harmonic Analysis
By Chengchun Hao. 2016
816 citations recorded by the source corpus.
Subfields: Cognitive Neuroscience, Computer Vision and Pattern Recognition, Music
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Cognitive Neuroscience
- Ricard Durall
- Luis Gravano
- Bernhard Schölkopf
- John Paparrizos
- Janis Keuper
- Margret Keuper
- Greg Yang
- Hadi Salman
In Computer Vision and Pattern Recognition
- Hadi Salman
- Greg Yang
- Ilya O. Tolstikhin
- Adam Scibior
- Carl-Johann Simon-Gabriel
- Bernhard Schölkopf
- William L. Hamilton
- Ricard Durall
In Music
- Ricard Durall
- Luis Gravano
- John Paparrizos
- Janis Keuper
- Margret Keuper
- Greg Yang
- Hadi Salman
- William L. Hamilton
Citations in the corpus
- Consistent Kernel Mean Estimation for Functions of Random Variables (2016, background): “Fifth line uses the fact that the Fourier (inverse) transform of a product equals the convolutional product of the (inverse) Fourier transforms (Katznelson, 2004, Theorem 1.4, and its generalisation to finite measures p.145).”
- Watch Your Up-Convolution: CNN Based Generative Deep Neural Networks Are Failing to Reproduce Spectral Distributions (2020, methodology): “Assuming a periodic signal and applying the convolution theorem [31], we get which equals to by Eq.”
- Iterative actions of normal operators (2016, background): “Hence, from the uniqueness theorem of the Fourier Stieltjes coefficients ([26], p.”
- Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation (2015, neutral): “To see this, note that Bochner’s theorem [71] implies that exp { −‖P‖(2)2 }”
- k-Shape: Efficient and Accurate Clustering of Time Series (2015, methodology): “The convolution theorem [39] states that the convolution of two time series can be computed as the Inverse Discrete Fourier Transform (IDFT) of the product of the individual Discrete Fourier Transforms (DFT) of the time series, where DFT is:”
- A Fine-Grained Spectral Perspective on Neural Networks (2019, background): “5 (Katznelson (2004)).”
- FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective (2023, neutral): “According to the convolution theorem [29] (see Appendix B), we can write the multiplication between F ( X ) and FGO S A,W in Fourier space as: where ( X ∗ κ )[ i ] denotes the convolution of X and κ .”
- Graph Representation Learning (2020, background): “We will not attempt to cover even a small fraction of the fields of digital signal processing, Fourier analysis, and harmonic analysis here, and we point the reader to various textbooks on these subjects [Grafakos, 2004, Katznelson, 2004, Oppenheim et al., 1999, Rabiner and Gold, 1975].”