The Fourier Transform and Its Applications

By R. Bracewell. 1966

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Citations in the corpus

Bayesian Neural Architecture Search using A Training-Free Performance Metric (2020, background): “Its study is interesting because, by adding sine waves, t is possible to approximate any periodic waveform [35].”
A Fourier Perspective on Model Robustness in Computer Vision (2019, background): “Let Ui,j ∈ Rd1×d2 be a real-valued matrix such that ‖Ui,j‖ = 1, and F(Ui,j) only has up to two non-zero elements located at (i, j) and the its symmetric coordinate with respect to the image center; we call these matrices the 2D Fourier basis matrices [4].”
The spatial resolution capacity of human foveal retina. (1989, background): “(1/2d) cycles per degree (c/deg) where d is the center-to-center spacing of cones in degrees of visual angle (Bracewell, 1965; Snyder & Miller, 1977; Yellott et al., 1984).”
Invariance properties of Gabor filter-based features-overview and applications (2006, background): “First, what makes these two domains, time and frequency, special should be considered, and is it reasonable to restrict the study to these domains alone.”
Antileakage Fourier transform for seismic data regularization (2005, background): “Shannon’s (1949) milestone paper set the foundation of information theory (Bracewell, 1965).”
The robustness of seismic attenuation measurements using fixed- and variable-window time-frequency transforms (2009, methodology): “w, and the Fourier transform Bracewell, 1978 is applied to the result:”
The Design and Use of Steerable Filters (1991, unknown): “are Hilbert transforms of each other [4]).”
Optimizing Spatial filters for Robust EEG Single-Trial Analysis (2008, methodology): “1: env c ( t , i ) ← envelope of X ( c , i )( t ) , calculated by Hilbert transform (e.g. [9]) and smoothed c) Selection of a Subset of Filters: The classical measure for the selection of CSP ﬁlters is based on the eigenvalues in (5).”
Statistical Analysis of the Multiple Scattering Radio Channel (2006, methodology): “The pdf of is given by the inverse Hankel transform [25]”
Foundations of Signal Processing (2014, background): “The text by Bracewell [10] is a classic; the material is written with engineering in mind, with plenty of intuition.”
CASA, the Common Astronomy Software Applications for Radio Astronomy (2022, methodology): “After visibilities are properly weighted, the next steps in the imaging process of interferometric data consists of gridding, Fourier transformation (Fourier 1878; Bracewell 2000), and normalization of the data.”
Fast and Robust Matching for Multimodal Remote Sensing Image Registration (2019, unknown): “theorem [29].”
Random error sampling-based recurrent neural network architecture optimization (2019, methodology): “roblem is based on two reasons. First, Camero et al. [10], [12] studied the problem so we can compare our results to theirs, and second, any periodic waveform can be approximated by adding sine waves [43]. Equation 3 expresses a sine wave as a function of time (t), where Ais the peak amplitude, fis ”