Discrete Lissajous Figures and Applications

In this paper, an innovative method based on an algorithm utilizing discrete convolutions of discrete-time functions is developed to obtain and represent discrete Lissajous and recton functions. They are actually discrete auto- and cross-correlation functions. The theory of discrete Lissajous figures is developed. The concept of rectons is introduced. The relation between the discrete Lissajous figures and autocorrelation functions is set. Some applications are described including phase, frequency, and period determination of periodic signals, time-domain characteristics (such as damping ratio) of a control system, and abnormality and spike detection within a signal, are described. In addition, an electrocardiogram signal with an abnormality of atrial fibrillation is given for abnormality detection by means of recton functions. An epileptic activity detection within an electroencephalography signal is also given.