In this book, the authors report the results obtained by the application of wavelet analysis to two physics experiments: the motion of variable mass pendulum and the motion of variable length pendulum. These two motions, which furnish non stationary signals for their motions, are analyzed by means of a comparative Fourier Transform and Wavelet Transform. Afterwards, interval arithmetic extensions for the standard algorithms for the decimated and undecimated unidimensional Haar wavelet transform, as well as the standard and non-standard formulations for the two-dimensional HWT, are presented. In one paper, wavelet analysis and other statistical tools are employed in order to analyse different aspects of Sicily temperature data. Sicily represents one of the hot spots for studying climate change in the Mediterranean area because of its vulnerability to desertification processes. The authors aim to highlight how wavelet transform can be employed to extract information from experimental results obtained by spectroscopic techniques, such as InfraRed, light and neutron scattering spectroscopies. In particular, this book shows how it is possible to characterize the registered spectral profiles by means of Wavelet Cross Correlation to evaluate spectra and the degree of similarity between images. Later, an iterative à trous coarsening algorithm combined with a wavelet extrapolation procedure is presented and analyzed to filter and identify the mean trend of simulated 1D data with non trivial boundary conditions. Results show that the wavelet extrapolation based algorithm considered for the data-driven analysis is robust and reliable, allowing for an increased confidence region of the wavelet transform. In the concluding chapter, the authors aim to show that the wavelet transform has several advantages and benefits over classical methods of spectral analysis and other approches.