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Complex weights factors (CWFs) that fully define the incident beam independent of the presence of a scatterer, may be represented mathematically by either a partial-wave series expansion (PWSE) of multipoles, or the method of angular…
Although frames, which are a generalization of bases, are important tools used in signal processing, their potential in other fields of engineering and applied mathematics (e.g. acoustics) has not been fully explored yet. Gabor frames, that…
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…
Compositional observations are an increasingly prevalent data source in spatial statistics. Analysis of such data is typically done on log-ratio transformations or via Dirichlet regression. However, these approaches often make unnecessarily…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
Spherical harmonics are a favorable technique for 3D representation, employing a frequency-based approach through the spherical harmonic transform (SHT). Typically, SHT is performed using equiangular sampling grids. However, these grids are…
The spectral theory on the S-spectrum was introduced to give an appropriate mathematical setting to quaternionic quantum mechanics, but it was soon realized that there were different applications of this theory, for example, to fractional…
A key aspect of machine learning models lies in their ability to learn efficient intermediate features. However, the input representation plays a crucial role in this process, and polyphonic musical scores remain a particularly complex type…
The quadratic scalar radar equations are obtained for SuperDARN radars that are suitable for the analysis and interpretation of experimental data. The paper is based on a unified approach to the obtaining radar equations for the monostatic…
We explore an unconventional bridge between quantum mechanical density matrices and sound by mapping elements of the density matrix and their phases to auditory signals, thus introducing a framework for Open Quantum Sonification. Employing…
In the rapidly evolving fields of virtual and augmented reality, accurate spatial audio capture and reproduction are essential. For these applications, Ambisonics has emerged as a standard format. However, existing methods for encoding…
We consider the scattering of acoustic perturbations in a presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
Spaces of harmonic functions in upper half-space with controlled growth near the boundary are described in terms of multiresolution approximations. The results are applied to prove the law of the iterated logarithm for the oscillation of…
We derive asymptotic estimates at infinity for positive harmonic functions in a large class of non-smooth unbounded domains. These include domains whose sections, after rescaling, resemble a Lipschitz cylinder or a Lipschitz cone, e.g.,…
Stochastic gradient descent (SGD) is a key ingredient in the training of deep neural networks and yet its geometrical significance appears elusive. We study a deterministic model in which the trajectories of our dynamical systems are…
This paper presents the 3D soundfield synthesis of the pressure field radiated by directional acoustic sources using both the multimodal method and higher-order ambisonics (HOA). Ambisonics is a technique for encoding and reproducing…
Decomposing the domain of a function into parts has many uses in mathematics. A domain may naturally be a union of pieces, a function may be defined by cases, or different boundary conditions may hold on different regions. For any…
We introduce an audio texture synthesis algorithm based on scattering moments. A scattering transform is computed by iteratively decomposing a signal with complex wavelet filter banks and computing their amplitude envelop. Scattering…
Mask processing in the time-frequency (T-F) domain through the neural network has been one of the mainstreams for single-channel speech enhancement. However, it is hard for most models to handle the situation when harmonics are partially…