Related papers: An optimally concentrated Gabor transform for loca…
The time-frequency content of a signal can be measured by the Gabor transform or windowed Fourier transform. This is a function defined on phase space that is computed by taking the Fourier transform of the product of the signal against a…
This article deals with the use of optimal lattice and optimal window in Discrete Gabor Transform computation. In the case of a generalized Gaussian window, extending earlier contributions, we introduce an additional local window adaptation…
Time-frequency analysis, such as the Gabor transform, plays an important role in many signal processing applications. The redundancy of such representations is often directly related to the computational load of any algorithm operating in…
We study functions whose time-frequency content are concentrated in a compact region in phase space using time-frequency localization operators as a main tool. We obtain approximation inequalities for such functions using a finite linear…
A Python package for the calculation of spectrograms with optimized time and frequency resolution for application in the analysis of numerical simulations on ultrashort pulse propagation is presented. Gabor's uncertainty principle prevents…
The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can…
We propose a method for automatic local time-adaptation of the spectrogram of audio signals: it is based on the decomposition of a signal within a Gabor multi-frame through the STFT operator. The sparsity of the analysis in every individual…
Based on a unique waveform with strong exponential localization property, an exact mathematical method for solving problems in signal analysis in time-frequency domain is presented. An analogue of the Gabor frame exposes the non-commutative…
We present an algorithm for sound analysis and resynthesis with local automatic adaptation of time-frequency resolution. There exists several algorithms allowing to adapt the analysis window depending on its time or frequency location; in…
In digital signal processing time-frequency transforms are used to analyze time-varying signals with respect to their spectral contents over time. Apart from the commonly used short-time Fourier transform, other methods exist in literature,…
In this paper we propose a method for automatic local time adap- tation of the spectrogram of an audio signal, based on its decomposition within a Gabor multi-frame. The sparsity of the analyses within each individual frame is evaluated…
We construct frames adapted to a given cover of the time-frequency or time-scale plane. The main feature is that we allow for quite general and possibly irregular covers. The frame members are obtained by maximizing their concentration in…
Many audio signal processing methods are formulated in the time-frequency (T-F) domain which is obtained by the short-time Fourier transform (STFT). The properties of the STFT are fully characterized by window function, number of frequency…
In the tradition of Gabor's 1946 landmark paper [1], we advocate a time-frequency (TF) approach to communications. TF methods for communications have been proposed very early (see the box History). While several tutorial papers and book…
Nonstationary signals are commonly analyzed and processed in the time-frequency (T-F) domain that is obtained by the discrete Gabor transform (DGT). The T-F representation obtained by DGT is spread due to windowing, which may degrade the…
We propose a new algorithm for time stretching music signals based on the theory of nonstationary Gabor frames (NSGFs). The algorithm extends the techniques of the classical phase vocoder (PV) by incorporating adaptive time-frequency (TF)…
We use time-frequency methods for the study of Fourier Integral operators (FIOs). In this paper we shall show that Gabor frames provide very efficient representations for a large class of FIOs. Indeed, similarly to the case of shearlets and…
We propose a time-varying optimal window width (TVOWW) selection scheme to optimize the performance of several nonlinear-type time-frequency analyses, including the reassignment method, and the synchrosqueezing transform (SST) and its…
Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply…
Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency-bands is preferable. This paper introduces a framework for efficient implementation of invertible signal…