Wavelet analysis in the field of coastal engineering

Abstract

Time-frequency analysis and digital signal processing are important tools in the field of coastal engineering. Both can be done using techniques like Fourier or wavelet analysis, however, analysts from this field experience a threshold to use wavelet analysis instead of their current methods, often Fourier-based. This is due to the lack of guidelines in the many choices accompanied by applying wavelets. This thesis investigates the added value of wavelet analysis in the field of coastal engineering. There are two wavelet transform types: continuous and discrete. The first one is most often used for time-frequency analysis. The range of signals that can be analysed more accurately has been increased by adding different signal extension methods and a method to quantify the effect of missing data points, based on the wavelets energy distribution. This allows a more accurate time-frequency analysis of time-series that cannot be assessed in the Fourier domain. The continuous wavelet coefficients can also be used for separating incident and reflected waves. Because the wave number of a wave is dependent on its frequency, the wavelet-based method performs equally well or worse for stationary signals than the current Fourier coefficient based method. For coastal engineering time-series with a changing mean water level, the time-dependency of the wavelet transform results in better separation than the Fourier coefficient based case. The discrete wavelet transform is mostly deployed in digital signal processing. Filtering in the discrete wavelet domain allows for better justification of the filtering of different signal elements such as noise and transients for signals that behave non-stationary, like measurements of impacts. The difference with the standard time or frequency domain methods lies within this justification, instead of a 'gut feeling' often used. Different algorithms to determine thresholds for use in noise filters have been tested. The soft applied universal threshold was the most effective of the compared algorithms in filtering noise from a non-stationary signal. In stationary signal cases, the low-pass filter showed better performance. The discrete wavelet decomposition offers many signal processing opportunities due to the wide range of wavelets that can be chosen.