Application of the Analytic Wavelet Transform for Time-Frequency Analysis of Impulsive Sound Signals 2005-01-2391

In highly transient sounds, time and frequency components are highly dependent of each other. A time-frequency (T-F) analysis is necessary for such signals. The wavelet transform is a T-F signal analysis algorithm which uses variable scales to satisfy both time and frequency resolution requirements more effectively. The analytic wavelet transform (AWT) is a wavelet transform that retains most of the basic features of the Fourier transform. We developed a form of AWT specifically made for acoustics applications. The method obtains the amplitude as well as phase of the sound signal as the Fourier transform does, however in the transient sense. Advantages of the method over the short time Fourier transform method, a commonly used Fourier transform based transient signal analysis method, are demonstrated using two impulsive signals as examples. Time-frequency domain representations of noise in a 3D contour plot and 1/3 octave time histories, their interpretations and potential applications are explained.