The mathematical concepts in the analysis of periodic functions

This paper discusses the mathematical concepts involved in the analysis of vibration data which are essentially steady state time-varying processes. The basic objective of vibration data analysis may be achieved by various means to describe time-varying functions such as displacement, velocity, acceleration, and describes the principle characteristics of these functions. This paper is restricted to a description of the basic principles and techniques of data analysis which represented by the two sine waves, each having a different frequency and amplitude. The waveform is the sum of the two sinusoids whose frequency difference is an integral multiple of the lowest frequency. For complete definition of the waveform it is necessary to specify the phase angle between the two sine waves, and the ratio of the displacement amplitudes.