We construct a sandpile model for evolution of the energy spectrum of the water surface waves in finite basins. This model takes into account loss of resonant wave interactions in discrete Fourier space and restoration of these interactions at larger nonlinearity levels. For weak forcing, the waveaction spectrum takes a critical ω shape where the nonlinear resonance broadening is equal to the F...

Most existing automatic chord recognition systems use a chromagram in front-end processing and some sort of classifier (e.g., hidden Markov model, Gaussian mixture model (GMM), support vector machine, or other template matching technique). The vast majority of front-end algorithms derive acoustic features based on a standard short-time Fourier analysis and on mapping energy from the power spect...

Signal processing is an important issue that should be considered prior to recording mechanomyographic (MMG) signals. The first studies in this area found that the fast Fourier transform and maximum entropy spectrum estimation techniques provided MMG frequency spectra that were very similar in shape. The shape of the spectrum from the maximum entropy spectrum estimation technique, however, was ...

We extend classical basis constructions from Fourier analysis to attractors for affine iterated function systems (IFSs). This is of interest since these attractors have fractal features, e.g., measures with fractal scaling dimension. Moreover, the spectrum is then typically quasi-periodic, but non-periodic, i.e., the spectrum is a “small perturbation” of a lattice. Due to earlier research on IF...

Nonlinear evolution causes the galaxy power spectrum to become broadly correlated over different wavenumbers. It is shown that prewhitening the power spectrum – transforming the power spectrum in such a way that the noise covariance becomes proportional to the unit matrix – greatly narrows the covariance of power. The eigenfunctions of the covariance of the prewhitened nonlinear power spectrum ...

I construct a sandpile model for evolution of the energy spectrum of the water waves in finite basins. This model takes into account loss of resonant wave interactions in discrete Fourier space and restoration of these interactions at larger nonlinearity levels. For weak forcing, the waveaction spectrum takes a critical ω shape where the nonlinear resonance broadening overcomes the effect of th...