Related papers: Sparse Frequency Analysis with Sparse-Derivative I…
State-of-the-art methods for Convolutional Sparse Coding usually employ Fourier-domain solvers in order to speed up the convolution operators. However, this approach is not without shortcomings. For example, Fourier-domain representations…
We propose a novel sparse representation for heavily underdetermined multichannel sound mixtures, i.e., with much more sources than microphones. The proposed approach operates in the complex Fourier domain, thus preserving spatial…
Frequency estimation is a fundamental problem in signal processing, with applications in radar imaging, underwater acoustics, seismic imaging, and spectroscopy. The goal is to estimate the frequency of each component in a multisinusoidal…
In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis to decompose the signal is not…
This paper proposes a novel, rigorous and simple Fourier-transformation approach to study resonances in a perfectly conducting slab with finite number of subwavelength slits of width $h\ll 1$. Since regions outside the slits are variable…
Fast Fourier Transform (FFT) is one of the most important tools in digital signal processing. FFT costs O(N \log N) for transforming a signal of length N. Recently, Sparse Fourier Transform (SFT) has emerged as a critical issue addressing…
Phaseless super-resolution refers to the problem of superresolving a signal from only its low-frequency Fourier magnitude measurements. In this paper, we consider the phaseless super-resolution problem of recovering a sum of sparse Dirac…
We develop an iterative, adaptive frequency sensing protocol based on Ramsey interferometry of a two-level system. Our scheme allows one to estimate unknown frequencies with a high precision from short, finite signals. It avoids several…
Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…
We present different computational approaches for the rapid extraction of the signal parameters of discretely sampled damped sinusoidal signals. We compare time- and frequency-domain-based computational approaches in terms of their accuracy…
Complex-valued sparse coding is a data representation which employs a dictionary of two-dimensional subspaces, while imposing a sparse, factorial prior on complex amplitudes. When trained on a dataset of natural image patches, it learns…
A Fourier transform method is introduced for a class of hybrid time-frequency methods that solve the acoustic scattering problem in regimes where the solution exhibits both highly oscillatory behavior and slow decay in time. This extends…
A heuristic procedure based on novel recursive formulation of sinusoid (RFS) and on regression with predictive least-squares (LS) enables to decompose both uniformly and nonuniformly sampled 1-d signals into a sparse set of sinusoids (SSS).…
A variational approach to reconstruction of phase and amplitude of a complex-valued object from Poissonian intensity observations is developed. The observation model corresponds to the typical optical setups with a phase modulation of…
Reconstruction fidelity of sparse signals contaminated by sparse noise is considered. Statistical mechanics inspired tools are used to show that the l1-norm based convex optimization algorithm exhibits a phase transition between the…
The short-time Fourier transform (STFT) represents a window of audio samples as a set of complex coefficients. These are advantageously viewed as magnitudes and phases and the overall distribution of phases is very often assumed to be…
The FFT algorithm that implements the discrete Fourier transform is considered one of the top ten algorithms of the $20$th century. Its main strengths are the low computational cost of $\mathcal{O}(n \log n$) and its stability. It is one of…
In this paper we deal with the linear frequency modulated signals and radar signals that are affected by disturbance which is the inevitable phenomenon in everyday communications. The considered cases represent the cases when the signals of…
Time-frequency analysis has been applied successfully in many fields. However, the traditional methods, like short time Fourier transform and Cohen distribution, suffer from the low resolution or the interference of the cross terms. To…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…