Although Fourier transformation is one of the basic tools and methods in signal analysis it also has intrinsic drawbacks, such as its inability to provide the temporal or spatial characteristics of a signal. Short-time Fourier transformation has certain improvements, but users can only obtain the time- and frequency-based aspects of a signal with limited precision. Wavelet transformation is a fast-developing and popular signal analysis method. Wavelet analysis allows the use of long time intervals for more precise low-frequency information, and short regions for high-frequency information. In this paper the development of wavelet transforms is reviewed, and the fundamental principles, concepts, calculation formulas and flowcharts are introduced. Four examples are included to illustrate the application of this method in modern engineering and its unique advantages in comparison to other techniques.