相关论文: Time-Frequency Localization and the Gabor Transfor…
We report experimental results of parallel measurement of spectral components of the light. The temporal fluctuations of an optical field mixed with a separate reference are recorded with a high throughput complementary metal oxide…
Fourier integral operators with sufficiently smooth phase act on the time-frequency content of functions. However time-frequency analysis has only recently been used to analyze these operators. In this paper, we show that if a Fourier…
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…
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…
The graph Fourier transform (GFT) is a fundamental tool in graph signal processing and has recently been extended to the graph fractional Fourier transform (GFRFT). Existing sampling methods in the GFRFT domain are primarily designed to…
We give a brief survey of recent results concerning almost diagonalization of pseudodifferential operators via Gabor frames. Moreover, we show new connections between symbols with Gevrey, analytic or ultra-analityc regularity and…
The problem of clock offset estimation in a two-way timing exchange regime is considered when the likelihood function of the observation time stamps is exponentially distributed. In order to capture the imperfections in node oscillators,…
Certain signal classes such as audio signals call for signal representations with the ability to adapt to the signal's properties. In this article we introduce the new concept of quilted frames, which aim at adaptivity in time-frequency…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
In this paper we address the problem of constructing a feature extractor which combines Mallat's scattering transform framework with time-frequency (Gabor) representations. To do this, we introduce a class of frames, called uniform covering…
Signal analysis is built upon various resolutions of the identity in signal vector spaces, e.g. Fourier, Gabor, wavelets, etc. Similar resolutions are used as quantizers of functions or distributions, paving the way to a time-frequency or…
This paper details the purpose, difficulties, theory, implementation, and results of developing a Fast Fourier Transform (FFT) using the prime factor algorithm on an embedded system. Many applications analyze the frequency content of…
This paper addresses the problem of expressing a signal as a sum of frequency components (sinusoids) wherein each sinusoid may exhibit abrupt changes in its amplitude and/or phase. The Fourier transform of a narrow-band signal, with a…
In this paper we show that the eigenfunctions can be found exactly for systems whose delay-Doppler spread function is concentrated along a straight line and they can be found in approximate sense for systems having a spread function…
A new method is proposed to determine the time-frequency content of time-dependent signals consisting of multiple oscillatory components, with time-varying amplitudes and instantaneous frequencies. Numerical experiments as well as a…
Fourier transform has become a basic tool for analyzing biological signals 1,2,3. Mostly a fast Fourier transform is computed for a finite sequence of data sample 4. This is the standard way apparatuses and modern computerized technology…
A finite-energy signal is represented by a square-integrable, complex-valued function $t\mapsto s(t)$ of a real variable $t$, interpreted as time. Similarly, a noisy signal is represented by a random process. Time-frequency analysis, a…
The quantum mechanical harmonic oscillator Hamiltonian generates a one-parameter unitary group W(\theta) in L^2(R) which rotates the time-frequency plane. In particular, W(\pi/2) is the Fourier transform. When W(\theta) is applied to any…
The covariance function and the variogram play very important roles in modelling and in prediction of spatial and spatio-temporal data. The assumption of second order stationarity, in space and time, is often made in the analysis of spatial…
Vertex-frequency analysis, particularly the windowed graph Fourier transform (WGFT), is a significant challenge in graph signal processing. Tight frame theories is known for its low computational complexity in signal reconstruction, while…