In this paper we propose a synthesis method using a force-based algorithm to control frequencies of multiple sine waves. In order to implement this synthesis method, we analyze an existing sound source using a fast Fourier transform (FFT). Spectral peaks which have large magnitudes are regarded as heavy partials and assigned large attractive forces. A few hundred sine waves with stationary ampl...

In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm or t-TNN for short. The twist tensor denotes a 3-way tensor representation to laterally store 2D data slices in order. On one hand, t-TNN convexly relaxes the tensor multi-rank of the twist tensor in the Fourier domain, which allows an efficient computation using FFT. On the o...

Wavelet methods give a exible alternative to Fourier methods in non-stationary signal analysis. The concept of band-limitedness plays a fundamental role in Fourier analysis. Since wavelet theory replaces frequency with scale, a natural question is whether there exists a useful concept of scale-limitedness. Obvious deenitions of scale-limitedness are too restrictive, in that there would be few o...

| Time-frequency representations (TFRs) are useful tools for examining non-stationary signals, but they are severely degraded by impulsive noise processes, such as those characterized by-stable models. In this paper, we propose two approaches to making TFRs more robust. We deene a robust STFT using myriad lters and show how it can be used to deene a \myriadized" PWD, or MyPWD, which can be tune...

We consider relativistic and ”semi-relativistic” models of radiative viscous compressible Navier-Stokes-Fourier system coupled to the radiative transfer equation extending the classical model introduced in [1] and we study some of its singular limits (low Mach and diffusion) in the case of well-prepared initial data and Dirichlet boundary condition for the velocity field. In the low Mach number...

Most of the commonly used stationary filtering techniques, performed either in the spatial or frequency domains, fail to produce good results for noisy signals with fast varying non-stationary structures. The filtering results could be improved by using space/spatial-frequency based non-stationary filters. Hence, a robust approach to space/spatial-frequency analysis of two-dimensional noisy sig...

We overview a new non-parametric method for estimating the time-varying spectrum of a non-stationary random process. Our method extends Thomson's powerful multiple window spectrum estimation scheme to the time-frequency and timescale planes. Unlike previous extensions of Thomson's method, we identify and utilize optimally concentrated Hermite window and Morse wavelet functions and develop a sta...