Signal analysis with classical Gabor frames leads to a fixed time-frequency resolution over the whole plane. To overcome limitations imposed by this rigidity, we propose an extension of theory that construction changing time or frequency. We describe resulting nonstationary and give explicit formula for canonical dual frame particular case, painless case. show wavelet transforms, constant-Q transforms more general filter banks may be modeled in framework frames. Further, present results...

In this paper, we present a new algorithm to estimate signal from its short-time Fourier transform modulus (STFTM). This is computationally simple and obtained by an acceleration of the well-known Griffin-Lim (GLA). Before deriving algorithm, will give interpretation GLA formulate phase recovery problem in optimization form. We then some experimental results where tested on various signals. It shows not only significant improvement speed convergence but it does as well recover signals with...

The Linear Time Frequency Analysis Toolbox is a MATLAB/Octave toolbox for computational time-frequency analysis. It intended both as an educational and tool. provides the basic Gabor, Wilson MDCT transform along with routines constructing windows (filter prototypes) manipulating coefficients. also bunch of demo scripts devoted either to demonstrating main functions toolbox, or exemplify their use in specific signal processing applications. In this paper we describe used algorithms,...

Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting frame operator. In this paper we develop systematically these notions, including their mutual relationship. We will show that are equivalent standard so concept gives a generalized way check condition, while offering advantage in sense preconditioning. Next, investigate weighted frames, particular relation frames. consider special case semi-normalized...

A noniterative method for the reconstruction of short-time fourier transform (STFT) phase from magnitude is presented. The based on direct relationship between partial derivatives and logarithm un-sampled STFT with respect to Gaussian window. Although theory holds in continuous setting only, experiments show that algorithm performs well even discretized (discrete Gabor transform) low redundancy using sampled window, truncated window other compactly supported windows such as Hann Due nature,...

We present an algorithm for removing time-frequency components, found by a standard Gabor transform, of ldquoreal-worldrdquo sound while causing no audible difference to the original after resynthesis. Thus, this representation is made sparser. The selection removable components based on simple model simultaneous masking in auditory system. Important goals were applicability any real-world music and speech sound, integrating mutual effects between coping with spread such operation,...

In this paper we examine the general theory of continuous frame multipliers in Hilbert space. These operators are a generalization widely used notion (discrete) multipliers. Well-known examples include Anti-Wick operators, STFT or Calder\'on- Toeplitz operators. Due to possible peculiarities underlying measure spaces, frames do not behave quite as well their discrete counterparts. Nonetheless, many results similar case proven for well, instance compactness and Schatten class properties....

House mice (Mus musculus) emit ultrasonic vocalizations (USVs), which are surprisingly complex and have features of bird song, but their functions not well understood. Previous studies reported mixed evidence on whether there sex differences in USV emission, though vocalization rate or other may depend upon potential receivers the same opposite sex. We recorded USVs wild-derived adult house (F1 wild-caught Mus musculus musculus), we compared males females response to a stimulus mouse same-...

Abstract Seismologists have to deal with overlapping and noisy signals. Techniques such as source separation can be used solve this problem. Over the past few decades, signal processing techniques for advanced significantly multi‐station settings. But not so many options are available when it comes single‐station data. Using Machine Learning, we demonstrate possibility of separating signals single‐station, one‐component seismic recordings. The technique that use is based on a dual‐path...

In this paper we deal with the theory of Hilbert–Schmidt operators, when usual choice orthonormal basis, on associated Hilbert spaces, is replaced by frames. We More precisely, provide a necessary and sufficient condition for an operator to be Hilbert–Schmidt, based its action elements frame (i.e. T [Formula: see text] if only sum squared norms applied finite). Also, construct Bessel sequences, frames Riesz bases operators using tensor products same sequences in spaces. state how inner...

Loosely speaking, a semi-frame is generalized frame for which one of the bounds absent. More precisely, given total sequence in Hilbert space, we speak an upper (resp. lower) if only bound valid. Equivalently, semi-frame, operator bounded, but has unbounded inverse, whereas lower operator, with bounded inverse. We study mostly semi-frames, both continuous case and discrete case, give some remarks dual situation. In particular, show that reconstruction still possible certain cases.

Certain mathematical objects appear in a lot of scientific disciplines, like physics, signal processing and, naturally, mathematics. In general setting they can be described as frame multipliers, consisting analysis, multiplication by fixed sequence (called the symbol), and synthesis. this paper we show surprising result about inverse such operators, if any, well new results core concept theory, dual frames. We that for semi-normalized symbols, any invertible multiplier always represented...

This paper describes a method for obtaining perceptually motivated and perfectly invertible time-frequency representation of sound signal. Based on frame theory the recent non-stationary Gabor transform, linear with resolution evolving across frequency is formulated implemented as non-uniform filterbank. To match human auditory resolution, transform uses Gaussian windows equidistantly spaced psychoacoustic "ERB" scale. Additionally, features adaptable redundancy. Simulations showed that...

We give a self-contained proof of recently established $\mathcal{B}(\mathcal{H})$-valued version Jaffards Lemma. That is, we show that the Jaffard algebra matrices, whose operator norms their respective entries decay polynomially off diagonal, is Banach which inverse-closed in $\mathcal{B}(\ell^2(X;\mathcal{H}))$ all bounded linear operators on $\ell^2(X;\mathcal{H})$, Bochner-space square-summable $\mathcal{H}$-valued sequences.

Associated with every separable Hilbert space $\mathcal{H}$ and a given localized frame, there exists natural test function Banach $\mathcal{H}^1$ distribution $\mathcal{H}^{\infty}$ so that $\mathcal{H}^1 \subset \mathcal{H} \mathcal{H}^{\infty}$. In this article we close some gaps in the literature rigorously introduce its weighted variants $\mathcal{H}_w^{\infty}$ slightly more general setting discuss of their properties. particular, compare underlying weak$^*$- norm topology associated...

Multipliers are operators that combine (frame-like) analysis, a multiplication with fixed sequence, called the symbol, and synthesis. They very interesting mathematical objects also have lot of applications for example in acoustical signal processing. It is known bounded symbols Bessel sequences guarantee unconditional convergence. In this paper we investigate necessary equivalent conditions convergence multipliers. particular show that, under mild conditions, unconditionally convergent...

To display the time and frequency content of a given signal large variety techniques exist.In this paper, we give an overview linear time-frequency representations, focusing mainly on two fundamental aspects.The first one is introduction flexibility, more precisely construction waveform systems that can be adapted to specific signals, or processing problems.To do this, base constructions frame theory, which allows lot options, while still ensuring perfect reconstruction.The second aspect...

We consider the quantum dynamics of a charged particle evolving under action constant homogeneous magnetic field, with emphasis on discrete subgroups Heisenberg group (in Euclidean case) and SL(2, R) Hyperbolic case). investigate completeness properties coherent states associated higher order hyperbolic Landau levels, partially extending classic results Perelomov Bargmann, Butera, Girardello Klauder. In case, our follow from identifying problem known theory Gabor frames. The for setting by...