Related papers: Time-Frequency analysis via the Fourier Representa…
Time-frequency scattering is a mathematical transformation of sound waves. Its core purpose is to mimick the way the human auditory system extracts information from its environment. In the context of improving the artificial intelligence of…
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…
Accurately calculating time delays between signals is pivotal in many modern physics applications. One approach to estimating these delays is computing the cross-spectrum in the time-frequency domain. Linear time-frequency representations,…
The short-time Fourier transform (STFT) is widely used for analyzing non-stationary signals. However, its performance is highly sensitive to its parameters, and manual or heuristic tuning often yields suboptimal results. To overcome this…
Identification of a transient gravitational-wave signal embedded into non-stationary noise requires the analysis of time-dependent spectral components in the resulting time series. The time-frequency distribution of the signal power can be…
The Heisenberg time-energy relation prevents determination of an atomic transition to better than the inverse of the measurement time. The relation generally applies to frequency estimation of a near-resonant field [1-3], since information…
A recently published method for audio style transfer has shown how to extend the process of image style transfer to audio. This method synthesizes audio "content" and "style" independently using the magnitudes of a short time Fourier…
We consider the inverse source problem of determining an acoustic source from multi-frequency phaseless far-field data. By supplementing some reference point sources to the inverse source model, we develop a novel strategy for recovering…
We present an uncertainty principle for graph signals in the vertex-time domain, unifying the classical time-frequency and graph uncertainty principles within a single framework. By defining vertex-time and spectral-frequency spreads, we…
We study the random sampling of the short-time Fourier transform of functions that are localized in a compact region in the time-frequency plane. We follow the approach introduced by Bass and Gr\"ochenig for band-limited functions, and show…
The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on…
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…
Spectrotemporal encoding of optical quantum information is emerging as a powerful tool in quantum information technology. Processing of spectrotemporal information has recently been demonstrated in multi-mode quantum memories, based on…
In this paper we construct directionally sensitive functions that can be viewed as directional time-frequency representations. We call such a sequence a rotational uniform covering frame and by studying rotations of the frame, we derive the…
Many real-world time series exhibit strong periodic structures arising from physical laws, human routines, or seasonal cycles. However, modern deep forecasting models often fail to capture these recurring patterns due to spectral bias and a…
We measure oscillator phase from the zero crossings of the voltage vs. time waveform of a spin torque nanocontact oscillating in a vortex mode. The power spectrum of the phase noise varies with Fourier frequency $f$ as $1/f^2$, consistent…
We propose spectral methods for long-term forecasting of temporal signals stemming from linear and nonlinear quasi-periodic dynamical systems. For linear signals, we introduce an algorithm with similarities to the Fourier transform but…
Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral characteristics of these time series data.…
Graph signal processing (GSP) facilitates the analysis of high-dimensional data on non-Euclidean domains by utilizing graph signals defined on graph vertices. In addition to static data, each vertex can provide continuous time-series…
Time-varying graph signals are alternative representation of multivariate (or multichannel) signals in which a single time-series is associated with each of the nodes or vertex of a graph. Aided by the graph-theoretic tools, time-varying…