Analyse van e-gitaar signalen in tijd- en frequentiedomein, in termen van snaar- en rand-dynamica
Analysis of e-guitar signals in time and frequency domain, in terms of string and boundary dynamics
B. de Koning (TU Delft - Electrical Engineering, Mathematics and Computer Science)
R van der Toorn – Mentor (TU Delft - Mathematical Physics)
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Abstract
In this thesis we examine various aspects of the output signal produced by the electrical pickup of an electric guitar. We do this by formulating a model of this output signal based on the one dimensional damped wave equation for the motion of one guitar string and (initially) a simple linear model for the output signal based on this motion. This model is compared to measurements of the output signal of a real guitar and their corresponding spectra. From this comparison it is concluded that the damping term in the damped wave equation is sufficient to roughly describe the decrease in amplitude over time of the envelope in the output signal of an electrical guitar.
The measured guitar signal also displays beating which has been considered to be caused by the interference of parallel and perpendicular modes on the guitar string with slightly differing frequencies. It is shown that the order of magnitude of this difference in frequencies between parallel and perpendicular modes is neither caused by different effective values of the damping coefficient nor by the influence of co-vibrating string boundaries. The last chapter gives a very simple method to introduce beating into the predicted signal. This is done by describing the motion of the string as occurring in a rotating plane in which the radial direction is given by the above mentioned model.