The visibility graph has gained traction as a method for time series analysis. Through this method, it is possible to detect or quantify non-linear behavior in a myriad of fields and applications. This thesis explores the variations of visibility graphs, describes how they are used in literature and investigates what lies at the foundation of the transformation from time domain to graph domain. The algorithm for the construction of a visibility graph is used as the starting point. Through mathematical derivation, claims can be made regarding the degree metric of a visibility graph. The average degree for a discrete random time series is defined with high accuracy. Using the inequality sets that can be derived from the adjacency matrix of a visibility graph, certain patterns can be identified as being unattainable for a visibility graph. The information retention is investigated by comparing the Shannon Entropy of both a time series and the visibility graph that is constructed from it. The loss of information can be quantified, but only for short discrete series with low sampling depth. These findings are reported in this thesis, along with some insights that could be the subject of further research to deepen the understanding or enhance the use of the visibility graph algorithm.

Laryngectomised people (LP) have many problems with speaking in terms of intelligibility, volume and effort it takes. This thesis describes the design and simulation of a voice enhancement device which will improve the speech of LP with respect to intelligibility and volume. It only describes the chosen hardware peripherals in order to record, process, amplify, and output the modified speech.
The recorded audio could be processed using a digital signal processor (DSP) that could be programmed such that it will filter the undesired noise and shift the pitch of the speaker's voice in real-time.
This thesis focuses on the real-time pitch shifting of the voice, the hardware choices and implementation of the sound output of the system, and the implementation of DSP of the Tracheo-Esophageal Speech Signal Amplifier (TESSA).
The real-time pitch shifting makes use of the Ocean algorithm, of which the principle is described, implemented and tested. Intelligibility tests are performed in order to find the optimal shifting parameters.