Related papers: Interpreting Frame Transformations as Diagonalizat…
This work identifies the general approach for linearising any power system component in the harmonic domain, that is with respect to its Fourier series coefficients. This ability enables detailed harmonic analysis, and is key as more power…
This paper develops a harmonic-domain framework for systems with variable fundamental frequency. A variable-frequency sliding Fourier decomposition is introduced in the phase domain, together with necessary and sufficient conditions for…
Transformer terminal equivalents obtained via admittance measurements are suitable for simulating high-frequency transient interaction between the transformer and the network. This paper augments the terminal equivalent approach with a…
In this paper we provide a complete link between dissipation theory and a celebrated result on stability analysis with integral quadratic constraints. This is achieved with a new stability characterization for feedback interconnections…
There are limitations on the extent to which manually constructed mathematical models can capture relevant aspects of legged locomotion. Even simple models for basic behaviors such as running involve non-integrable dynamics, requiring the…
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…
We characterize the pre-softmax attention matrix $\mathbf{QK^\top}$ in transformers as an associative memory matrix encoding pairwise associations between input features. By decomposing this matrix into its symmetric and skew-symmetric…
We introduce transfer matrices to describe the motion of particles in the vicinity of the stable and unstable fixed points of longitudinal phase space and use them to analyze the transfer of bunches between radio-frequency systems operating…
Transfer matrices and matrix product operators play an ubiquitous role in the field of many body physics. This paper gives an ideosyncratic overview of applications, exact results and computational aspects of diagonalizing transfer matrices…
Accurate upsampling of Head-Related Transfer Functions (HRTFs) from sparse measurements is crucial for personalized spatial audio rendering. Traditional interpolation methods, such as kernel-based weighting or basis function expansions,…
Besides the center of inertia (COI) frequency dynamics addressed in Part I, the spatial frequency variation in power systems with grid-following (GFL) converters is also crucial. Part II revisits the effect of GFLs on frequency spatial…
Finding the consequences of symmetry for open system quantum dynamics is a problem with broad applications, including describing thermal relaxation, deriving quantum limits on the performance of amplifiers, and exploring quantum metrology…
In this paper, we show a new relation between phase transition in one-dimensional Statistical Mechanics and the multiplicity of the dimension of the space of harmonic functions for an extension of the classical transfer operator. We…
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
The short-time Fourier transform (STFT) usually computes the same number of frequency components as the frame length while overlapping adjacent time frames by more than half. As a result, the number of components of a spectrogram matrix…
We defend the Fock-space Hamiltonian truncation method, which allows to calculate numerically the spectrum of strongly coupled quantum field theories, by putting them in a finite volume and imposing a UV cutoff. The accuracy of the method…
Conformal techniques, based on the covariance of Maxwell's electrodynamics under the full conformal group in four spacetime dimensions, are discussed in relation with the constant input impedance properties of frequency-independent…
In room acoustic environments, the Relative Transfer Functions (RTFs) are controlled by few underlying modes of variability. Accordingly, they are confined to a low-dimensional manifold. In this letter, we investigate a RTF inverse…
A key factor that generates significant interest in reset control systems, especially within industrial contexts, is their potential to be designed using a frequency-domain loop-shaping procedure. On the other hand, formulating and…
A joint frame and carrier frequency synchronization algorithm for coherent optical systems, based on the digital computation of the fractional Fourier transform (FRFT), is proposed. The algorithm utilizes the characteristics of energy…