## 4 Physical Audio Features Extraction Techniques
### Wavelet-Based Physical Features  
A Wavelet is a mathematical function used to divide a given function or continuous-time signal into different scale components. The Wavelet transform (WT) has advantages over the traditional Fourier transform for representing functions that have discontinuities and sharp peaks, and for accurately deconstructing and reconstructing finite, non-periodic and/or non-stationary signals ([PERSON] [113]). In the work by [PERSON] and [PERSON] [114], a link between auditory functions and Wavelet analysis was provided, while in the work by [PERSON] _et al._[115] an analytical framework to model the early stages of auditory processing, based on Wavelet and multiresolution analysis was proposed. In the following paragraphs, we describe the most commonly used wavelet-based physical frequency features. * **Wavelet-based direct approaches:** different type or families of wavelets have been used and defined in the literature in the field of audio processing. Daubechies wavelets have been used in blind source speech separation (see the work by [PERSON] and [PERSON] [116]) and Debechies together with Haar wavelets have been used in music classification ([PERSON] _et al._[117]), while Coiflets wavelet have been applied recently to de-noising of audio signals ([PERSON] _et al._[118]). Other approaches like Daubechies Wavelet coefficient histogram (DWCH) features, are defined as the first three statistical moments of the coefficient histograms that represent the subbands obtained from Daubechies Wavelet audio signal decomposition (see [PERSON] _et al._[40,119]). They have been applied in the field of speech recognition ([PERSON] _et al._[120]), music analysis applications such as genre classification, artist style identification and emotion detection (as in [PERSON] _et al._[40,119,121], [PERSON] and [PERSON] [122], [PERSON] _et al._[109]) or mood classification ([PERSON] _et al._[86]). Also, in the work by [PERSON] and [PERSON] [123], different wavelet families (like Daubechies, symlet, coiflet, biorthogonal, stationary and dmer) are used in audio steganography (an application for hiding data in cover speech which is imperceptible from the original audio). * **Hurst parameter features:** or pH for short, is a time-frequency statistical representation of the vocal source composed of a vector of Hurst parameters (defined by [PERSON] [25]), which was computed by applying a wavelet-based multidimensional transformation of the short-time input speech in the work by [PERSON] [124]. Thanks to its statistical definition, pH is robust to channel distortions as it models the stochastic behavior of input speech signal (see [PERSON] _et al._[125], or [PERSON] _et al._[126]). pH was originally applied as a means to improve speech-related problems, such as text-independent speaker recognition [124], speech emotion classification [125,126], or speech enhancement [127]. However, it has also been applied to sound source localization in noisy environments recently, as in the work by [PERSON] and [PERSON] [128]. An alternative means to represent signals using a finite dictionary of basis functions (or atoms) is matching pursuit (MP), described by [PERSON] in [129], an algorithm that provides an efficient way of sparsely decomposing a signal by selecting the \"best\" subset of basis vectors from a given dictionary. The selection of the \"best\" elements in the dictionary is based on maximizing the energy removed from the residual signal at each step of the algorithm. This allows obtaining a reasonable approximation of the signal with a few basis functions, which provides an interpretation of the signal structure. The dictionary of basis functions can be composed of Wavelet functions, Wavelet packets, or Gabor functions, to name a few. The following paragraphs describe some relevant audio features using MP-based signal decompositions.