Signal Dynamics as Superpositions of Sinusoidal Waves in the Time Domain

Abstract

The basis of waveform representation is a sinusoidal function. This chapter introduces the basic nature of compound signals, that is, superpositions of sinusoidal waves. The time envelopes of the compound signals represent the signal dynamics arising from temporal changes in magnitude. The local spectral characteristics like the group delay determines the time-shift of the envelope as well as the dynamic range for the envelope given by the spectral characteristics of the magnitude of the sinusoidal components. Auto-correlation functions provide means to estimate the period of the compound signal even under the missing fundamental condition, in which the component corresponding to the fundamental frequency is lost. The auto-correlation analysis shows that a nonharmonic signal is, from a practical point of view, an example of a missing fundamental condition in which the fundamental is lower than the audible range. Cross-correlation analysis for the normal and time-reversed signals is a possible way to evaluate symmetry in the waveform in the time domain.