Signal-processing of audio for speech-recognition

The transcription of voice using neural networks is a technique that deserves attention, as speech assistants are becoming increasingly popular. Neural networks have often difficulty with determining the differences between a talking person and noise. Humans have a much better understanding of this and could possibly apply their knowledge of the...

Fourier analysis on finite groups and the irreducible representations of the symmetric group

In this paper we will naturally extend the concept of Fourier analysis to functions on arbitrary groups. We will generalise the idea of a convolution and try to find a formula for Fourier coefficients in such way that the coefficients of the convolution can easily be calculated. In the first section we will start off in familiar territory as we...

Scaling limit of the odometer of correlated Gaussians on the torus

In the divisible sandpile model, we consider a collection of i.i.d. Gaussian heights on a finite graph. It was shown by Levine et al. (2015) that the odometer function in this case equals a discrete, bi-Laplacian field. Subsequently, Cipriani et al. (2016) proved that the scaling limit of the odometer is a continuum bi-Laplacian field, this time...

Boundary values of analytic functions on the disc

In this bachelor's thesis we will solve the Dirichlet problem with an L^p(T) boundary function. First, we will focus on the holomorphic version of the Dirichlet problem and introduce Hardy space theory, from which will follow a sufficient condition on the Fourier coefficients of the boundary function. Then we will prove the...