A comparative analysis of mathematical transformations for signal processing

A signal is a physical quantity that represents information and is also a carrier of information. As signals are indispensable in every aspect of life, signal processing has always been a hot topic of research. With the continuous improvement of signal processing technology, it is used in a wide range of fields, such as digital filters, speech signal processing, image signal processing, biomedical aspects, etc. This paper first introduces the types of signals and basic concepts and some modern signal processing techniques which are commonly appeared. Afterwards, the principles and characteristics of the Fourier Transform, the Wavelet Transform and the Hilbert-Huang Transform are described. Furthermore, the advantages and disadvantages of the three signal processing methods and their respective fields of application are derived by means of comparative analysis. At the same time, the connections and unique features that exist between them are explained. Finally, the paper gives a conclusion and an outlook.