The discrete wavelet transform in S
By Guy P. Nason, Bernard Walter Silverman. 1994
Abstract The theory of wavelets has recently undergone a period of rapid development. We introduce a software package called wavethresh that works within the statistical language S to perform one- and two-dimensional discrete wavelet transforms. The transforms and their inverses can be computed using any particular wavelet selected from a range of different families of wavelets. Pictures can be drawn of any of the one- or two-dimensional wavelets available in the package. The wavelet coefficients can be presented in a variety of ways to aid in the interpretation of data. The package's wavelet transform “engine” is written in C for speed and the object-oriented functionality of S makes wavethresh easy to use. We provide a tutorial introduction to wavelets and the wavethresh software. We also discuss how the software may be used to carry out nonlinear regression and image compression. In particular, thresholding of wavelet coefficients is a method for attempting to extract signal from noise and wavethresh i...
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Citations in the corpus
- DelightfulTTS 2: End-to-End Speech Synthesis with Adversarial Vector-Quantized Auto-Encoders (2022, methodology): “To alleviate highfrequency loss, we further replace problematic average pooling method with discrete wavelet transform [20, 18] as the down sampling method, which is an effective way of down sampling non-stationary signals into several frequency sub-bands.”
- Concordance and discordance in cosmology (2018, methodology): “We thus require the Gelman and Rubin R test [64, 65] to satisfy R − 1 < 0.”
- Multiresolution models for nonstationary spatial covariance functions (2002, methodology): “The W-wavelet is implemented in the Fields package [ 9 ] for the Splus and R statistical environments.”
- Extending the Scope of Wavelet Regression Methods by Coefficient-Dependent Thresholding (2000, methodology): “Universal thresholds are used in each case; for the bottom figures these are noise-proportional.”
- Using unlabelled data to update classification rules with applications in food authenticity studies (2006, methodology): “The wavelet decomposition was completed by using the wavethresh library in R (Nason, 1993; Nason and Silverman, 1994).”
- Generalized fiducial inference for wavelet regression (2009, background): “The five test functions were Block, Bumps, Doppler and Heavisine of Donoho & Johnstone (1994), and the piecewise polynomial function Ppoly of Nason & Silverman (1994).”
- Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum (2000, unknown): “; $ & ( G.- $ $ 6 $ $ H $ !”
- Wavelets, approximation, and statistical applications (2013, methodology): “The second technique of handling the non-equispaced case was proposed by Neumann & Spokoiny (1995). It is related to the Gasser-Müller kernel regression estimator, see Härdle (1990, Section 3.”
- Real nonparametric regression using complex wavelets (2004, unknown): “The simulated data sets consisted of the standard test signals blocks, bumps, Doppler, heavisine (Donoho and Johnstone, 1994) and ppoly (Nason and Silverman, 1994), corrupted by independent Gaussian noise as in equation (1).”