Wavelets Analysis
Maria Cristina Mariani, Osei Kofi Tweneboah, Maria Pia Beccar-Varela · 2021
This chapter examines another transformation technique, namely the wavelets transform. An advantage of the wavelets transform is the fact that is localized both in the frequency and time domain. As a mathematical tool, wavelets can be used to extract information from various kinds of data, including digital signals, images, and several others. A discrete wavelet transform decomposes a signal into a set of mutually orthogonal wavelet basis functions. The Haar functions in fact are very useful for demonstrating the basic characteristics of wavelets. Daubechies wavelets are localized in the temporal domain, and approximately localized in the frequency domain. The chapter discusses wavelets techniques used to analyze the seismograms of a set of mining explosions, reported in catalogs as earthquakes, and compared the results with natural earthquakes that occurred in the same region. The wavelet transform can be used to detect cracks in frame structures, such as beams and plane frames.