Wavelet Analysis

Wavelets are short oscillating functions which are well localized in time and frequency with finite energy and a zero mean (admissibility condition). Wavelet analysis delivers very good results for analysis of transient signals, but, contrary to an auditory spectrogram (ASP), the results are not hearing based.

dBSONIC supports the Continuous Wavelet Transform (CWT) as well as the Discrete Wavelet Transform (DWT). For the CWT you can select in dBSONIC between different types of the Morlet wavelet and the Derivative of Gaussian wavelets. For the DWT the Daubechie wavelets can be applied in dBSONIC. The DWT is defined for dyadic sampling of time and scale, i.e. each scale is the previous doubled lower scale. By doubling the scale, the frequency resolution is doubled and the time resolution is halfed. Therefore also the time sampling rate is halfed for every higher scale. The DWT is similar to a non-redundant octave filter bank analysis which is computational very efficient.

In contrast to the wavelet transform the time and frequency resolution of the STFT is fixed and defined by the length and shape of the window (for example 1024 samples Hanning) used. The wavelet transform can be displayed as a scalogram where color coded wavelet power spectra are shown versus time. Wavelets are often normalized so that they have unit energy at all scales.

In dBSONIC the wavelets are normalized to have unit gain at their center frequencies in order to get comparable results to other time-frequency analyses in dBSONIC.