Introducing phase correlation into the course of signals and systems

Phase correlation has been widely used in many areas, such as, time delay estimation, motion estimation for video coding, and image registration. The fundamental of phase correlation is some basic properties of the Fourier Transform. It is proposed in this paper to introduce phase correlation into the course of signals and systems, and it is suggested that phase correlation be taught just on finishing the following properties of the Fourier Transform: linearity, time shifting, frequency shifting, scaling and symmetry. In this paper, phase correlation is proved as one property (called as phase correlation property) of the Fourier Transform, and examples are used to demonstrate the efficiency of the time delay estimation method based on the phase correlation property, even when noises exist in the delayed version of the original signal. Some problems for homework are also provided. These contents were first taught experimentally in two classes including 73 students, at Yangtze University in the Spring of 2010, and the results are satisfactory.