Discrete Lissajous and Recton Functions: A New Method for Frequency Response Measurements

Abstract An innovative and completely new technique so called discrete Lissajous functions and recton functions for signal analysis and measurement is explained. The contribution of the study is that it is a new digital method of obtaining information on frequency, change of frequency, phase and phase shift as well as auto-correlation, cross-correlation and energy functions of signals in digital form on-line that may be difficult to be provided in analog form and available for measurement and control applications at each sampling instance directly. The discrete Lissajous figures and recton functions can also be sketched in digital image form for further analysis of signals and systems. They are based on an algorithm utilizing discrete convolutions of discrete time signals. They can be depicted in 3D form. They give more information than classical analog Lissajous figures obtained on an oscilloscope screen. They can be used for several applications from chaotic systems to biomedical applications requiring to finding correlations, energies as well as frequency and phase information of the signals and controlling such systems. In this study, the application of them to systems steady-state, mainly frequency response analysis is explained after giving basic definitions.