Wavelet-Based Visualization, Separation, and Synthesis Tools for Sound Quality of Impulsive Noises

Recent applied mathematics research on the properties of the invertible shift-invariant discrete wavelet transform has produced new ways to visualize, separate, and synthesize impulsive sounds, such as thuds, slaps, taps, knocks, and rattles. These new methods can be used to examine the joint time-frequency characteristics of a sound, to select individual components based on their time-frequency localization, to quantify the components, and to synthesize new sounds from the selected components. The new tools will be presented in a non-mathematical way illustrated by two real-life sound quality problems, extracting the impulsive components of a windshield wiper sound, and analyzing a door closing-induced rattle.