<p style='text-indent:20px;'>In this paper, we consider a quaternionic short-time Fourier transform (QSTFT) with normalized Hermite functions as windows. It turns out that such is based on the recent theory of slice polyanalytic quaternions. Indeed, will use notions true and full Fock spaces Segal-Bargmann transforms. We prove new properties QSTFT including Moyal formula, reconstruction f...

Fourier Wavefront Reconstruction Over a Rectangular Pupil The iterative and boundary methods developed here for circular and elliptical pupils are based on a method to reconstruct the wavefront over the rectangular pupil. To fully understand this development, it is necessary to first summarize the approach used by Freischlad and Koliopoulos to derive an inverse spatial filter to reconstruct a w...

The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the “optimal” solution according to a maximum-entropy selection criterion.

i M. Modarres-Hashemi is with the ECE Department of Isfahan University of Technology, Isfahan, Iran (email: [email protected]) ii M. Dorostgan is with the ECE Department of Isfahan University of Technology, Isfahan, Iran ( email:[email protected]) iii Corresponding Author, M. M. Naghsh is with the ECE Department of Isfahan University of Technology, Isfahan, Iran (email: mm_naghsh@...

In this paper we extend analytic signal method to the functions in many dimensions. First it is shown how to obtain separate phase-shifted components and how combine them to obtain signal's envelope, instantaneous frequencies and phases in many dimensions. Second, we show that phase-shifted components may be obtained by positive frequency restriction of the Fourier transform defined in the alge...

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In this paper, we consider the underdetermined convolutive audio source separation (UCASS) problem. In the STFT domain, we consider both source signals and mixing filters as latent random variables, and we propose to estimate each source image, i.e. each individual sourcefilter product, by its posterior mean. Although, this is a quite straightforward application of the Bayesian estimation theor...

| 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...

Exponentially damped sinusoids (EDS) model-based analysis of sound signals often requires a precise estimation of initial amplitudes and phases of the components found in the sound, on top of a good estimation of their frequencies and damping. This can be of the utmost importance in many applications such as high-quality re-synthesis or identification of structural properties of sound generator...

AbstructWe consider a multidimensional parameter space formed by inner products of a parameterizable family of chirp functions with a signal under analysis. We propose the use of quadratic chirp functions (which we will call q-chirps for short), giving irise to a parameter space that includes both the time-frequency plane and the time-scale plane as 2-D subspaces. The parameter space contains a...