Signal Dynamics for Time and Frequency Domains

Abstract

This chapter describes the basic nature of signal dynamics (that is, changes in the signal within the time and frequency domains). Typical examples of modifications in the signal dynamics arise from ambient noise and sound path. The random nature of noise is understood as processes in addition and multiplication. Random noise processes are modeled as unpredictable external sources to a linear system. Information concerning the sound path for waves of a linear system can be obtained even when a nondeterministic source excitation is present from the statistical frequencies (histogram) with respect to frame-wise power spectral maxima. The frame-wise maxima interpolated from the frame-wise spectra are also informative in source signature analyses, for example, in the temporally changing fundamental frequency tracking of musical instruments, speech, and singing voices. Power spectral maxima characterize the resonance structures in the source or sound path structures. The sound path is quite likely determining those resonances which are with close frequencies. Overlapping resonance modes require, in general, the decomposition of the modal responses. With inspiration from human hearing, a filter set made of three narrow-band filters is a possible way to decompose the overlapping response. Another way is solving a set of linear equations that represents overlapping modes based on the least-squares criterion—referred here as clustered line spectral modeling (CLSM). The envelope representing the signal dynamics in the time domain can be characterized from CLSM because the envelope is composed of clustered frequency components around the resonance frequency. When extended into the time domain, CLSM is here referred to as CTSM (clustered time sequence modeling). Signature analysis of the piano-string vibration provides a nice example of CLSM and CTSM.