ABSTRACT
Many objects have a periodic behavior and thus show a unique characteristic in the frequency domain. For example, human sounds have a range of frequencies that are different from those of some animals. Objects in the space including the earth move at different frequencies. A new object in the space can be discovered by observing its unique movement frequency, which is different from those of known objects. Hence, the frequency characteristic of an object can be useful in identifying an object. Wavelet analysis represents time series data in the time–frequency domain using data characteristics over time in various frequencies, and thus allows us to uncover temporal data patterns at various frequencies. There are many forms of wavelets, e.g., Haar, Daubechies, and derivative of Gaussian (DoG). In this chapter, we use the Haar wavelet to explain how wavelet analysis works to transform time series data to data in the time–frequency domain. A list of software packages that support wavelet analysis is provided. Some applications of wavelet analysis are given with references.
