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The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization…
Spectrograms visualize the frequency components of a given signal which may be an audio signal or even a time-series signal. Audio signals have higher sampling rate and high variability of frequency with time. Spectrograms can capture such…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
The analysis of the time-frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative…
In this work, we propose a time-varying wave-shape extraction algorithm based on a modified version of the adaptive non-harmonic model for non-stationary signals. The model codifies the time-varying wave-shape information in the relative…
Disentangling and recovering physical attributes, such as shape and material, from a few waveform examples is a challenging inverse problem in audio signal processing, with numerous applications in musical acoustics as well as structural…
We develop a framework to track the structure of temporal networks with a signal processing approach. The method is based on the duality between networks and signals using a multidimensional scaling technique. This enables a study of the…
The paper aims at proposing the first shape identification and classification algorithm in echolocation. The approach is based on first extracting geometric features from the reflected waves and then matching them with precomputed ones…
The concept of a common modulated oscillation spanning multiple time series is formalized, a method for the recovery of such a signal from potentially noisy observations is proposed, and the time-varying bias properties of the recovery…
The analysis of multivariate time series data is challenging due to the various frequencies of signal changes that can occur over both short and long terms. Furthermore, standard deep learning models are often unsuitable for such datasets,…
In this paper, we establish a connection between the recently developed data-driven time-frequency analysis \cite{HS11,HS13-1} and the classical second order differential equations. The main idea of the data-driven time-frequency analysis…
We present a novel topological framework for analyzing functional brain signals using time-frequency analysis. By integrating persistent homology with time-frequency representations, we capture multi-scale topological features that…
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…
The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the…
Resonances are common in wave physics and their full and rigorous characterization is crucial to correctly tailor the response of a system in both time and frequency domains. However, they have been conventionally described by the quality…
The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously can be presented in the frequency domain clearly and precisely by using the Square Wave Transform (SWT) described here. As an example, the SWT…
The utilization of millimeter wave frequency bands is expected to become prevalent in the following communication systems. However, generating and transmitting communication signals over these frequencies is not as straightforward as in…
I define here a novel function on a modeled space of gravitational-wave signals, before studying its properties as a statistic for detection, as an objective function for identification, and as an effective likelihood function for…
Thanks to novel, powerful brain activity recording techniques, we can create data-driven models from thousands of recording channels and large portions of the cortex, which can improve our understanding of brain-states neuromodulation and…
Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern,…