Essays about: "Hilbert transform"

Showing result 1 - 5 of 11 essays containing the words Hilbert transform.

1. 1. Investigation of soliton equations with integral operators and their dynamics

   University essay from KTH/Skolan för teknikvetenskap (SCI)

   Author : Ruben Vikars Hall; Carl Svennerstedt; [2023]
   Keywords : Soliton; Calogero-Moser-Sutherland system; Lax pair; Hilbert transform; Szegö projection; Benjamin-Ono equation; Non-chiral Intermediate long-wave equation; Szegö equation;

   Abstract : We present Lax pairs and functions called Lax functions corresponding to Calogero- Moser-Sutherland (CMS) systems. We present the Benjamin-Ono (BO) equation and a pole ansatz to the BO equation, constructed from a specific type of Lax function called a special Lax function corresponding to Rational and Trigonometric CMS systems. READ MORE

3. 2. Gravity water waves over constant vorticity flows: from laminar flows to touching waves

   University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

   Author : Francisco Gonçalves Jorge Dias de Carvalho; [2023]
   Keywords : Partial differential equations; Water waves; Euler equations; Free boundary problem; Bifurcation theory; Nonlinear functional analysis; Hilbert transform; Mathematics and Statistics;

   Abstract : In a recent paper, Hur and Wheeler proved the existence of periodic steady water waves over an infinitely deep, two-dimensional and constant vorticity flow and subject to gravity whose profile overhangs, among which, waves whose surface touches at a point, enclosing a bubble of air. We take this further, proving the existence of a continuous curve of water waves from a laminar flow up to a touching wave for fixed non-zero gravity. READ MORE

4. 3. An operator theoretic approach to the Riemann Hypothesis

   University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

   Author : Ramon Arjan van de Scheur; [2023]
   Keywords : Riemann hypothesis; Prime number theorem; Prime number theorem for arithmetic progressions; operator theoretic equivalent; compact operator; prime-counting function; Chebyshev function; Laplace transform; Fourier transform; convolution operator; weak topology; strong topology; compact perturbation; Tauberian theorem; Poisson kernel; holomorphic; self-adjoint; spectrum; trace; Mathematics and Statistics;

   Abstract : In 2023 an operator theoretic approach to the Prime Number Theorem was introduced by Olsen. In this thesis this approach is examined and applied to give a new, operator theoretic, proof of a different version of the Prime Number Theorem and of the Prime Number Theorem for arithmetic progressions. READ MORE

5. 4. Study of neural correlates of attention in mice with spectro-spatio-temporal approaches

   University essay from KTH/Skolan för datavetenskap och kommunikation (CSC)

   Author : Cantin Ortiz; [2018]
   Keywords : gamma; bursts; neuroscience; attention; mice; LFP; gamma bursts; local field potential; phase randomization; cognition; cognitive process; modulation; spike; neuron; prefrontal cortex; PFC; pre-frontal; tetrode; filtering; Hilbert transform; recordings; oscillation; gamma band;

   Abstract : While signatures of attention can be observed in widespread areas within and outside of cortex, the control of attention is thought to be regulated by higher cognitive brain areas, such as the prefrontal cortex. In their recent study on mice Kim et al. READ MORE

6. 5. Hilbert Transform : Mathematical Theory and Applications to Signal processing

   University essay from Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakulteten

   Author : Måns Klingspor; [2015]
   Keywords : Hilbert transform; Hilbert-Huang transform; Electrocardiography; Electrocardiogram; ECG; EKG; Nonstationary processes; Hilbert spectrum; Modulation; Single-sideband modulation; QRS complex; QRS; QRS detection; SSB;

   Abstract : The Hilbert transform is a widely used transform in signal processing. In this thesis we explore its use for three different applications: electrocardiography, the Hilbert-Huang transform and modulation. For electrocardiography, we examine how and why the Hilbert transform can be used for QRS complex detection. READ MORE