## 4 Physical Audio Features Extraction Techniques
### Time Domain Physical Features
#### 4.1.4 Rhythm-Based Physical Features  
Rhythm represents an relevant aspect of music and speech, but it can also be significant in environmental and human activity related sounds (e.g., the sound of a train, finger tapping, _etc._), since it characterizes structural organization of sonic events (changes in energy, pitch, timbre, _etc._) along the time axis. Since the review by [PERSON] _et al._[17], there have been little significant contributions to the derivation of rhythm-based features. Thus, the following paragraphs describe the most relevant and classic rhythm-based features found in the literature.  
* **Pulse metric:** this is a measure that uses long-time band-passed autocorrelation to determine how rhythmic a sound is in a 5-second window (as defined by [PERSON] and [PERSON] [61]). Its computation is based on finding the peaks of the output envelopes in six frequency bands and its further comparison, giving a high value when all subbands present a regular pattern. This feature has been used for speech/music discrimination.
* **Pulse clarity:** it is a high-level musical dimension that conveys how easily in a given musical piece, or a particular moment during that piece, listeners can perceive the underlying rhythmic or metrical pulsation (as defined in the work by [PERSON] _et al._[62]). In that work, the authors describe several descriptors to compute pulse clarity based on approaches such as the analysis of the periodicity of the onset curve via autocorrelation, resonance functions, or entropy. This feature has been employed to discover correlations with qualitative measures describing overall properties of the music used in psychology studies in the work by [PERSON] _et al._[63].
* **Band periodicity:** this is a measure of the strength of rhythmic or repetitive structures in audio signals (see [PERSON] _et al._[64]). Band periodicity is defined within a frequency band, and it is obtained as the mean value along all the signal frames of the maximum peak of the subband autocorrelation function.  
* **Beat spectrum/spectrogram:** it is a two-dimensional parametrization based on time variations and lag time, thus providing an interpretable representation that reflects temporal changes of tempo (see the work by [PERSON] [22; 65]). Beat spectrum shows relevant peaks at rhythm periods that match the rhythmic properties of the signal. Beat spectrum can be used for discriminating between music (or between parts within an entire music signal) with different tempo patterns.
* **Cyclic beat spectrum:** or CBS for short, this is a representation of the tempo of a music signal that groups multiples of the fundamental period of the signal together in a single tempo class ([PERSON] _et al._[66]). Thus, CBS gives a more compact representation of the fundamental beat period of a song. This feature has been employed in the field of audio retrieval.
* **Beat tracker:** this a feature is derived following an algorithmic approach based on signal subband decomposition and the application of a comb filter analysis in each subband (see [PERSON] [67]). Beat tracker mimics at large extent the human ability to track rhythmic beats in music and allows obtaining not only tempo but also compute beat timing positions.
* **Beat histogram:** it provides a more general tempo perspective and summarizes the beat tempos present in a music signal ([PERSON] and [PERSON] [28]). In this case, Wavelet transform (see Section 4.3 for further details) is used to decompose the signal in octaves for performing subsequent accumulation of the most salient periodicities in each subband to generate the so-called beat histogram. This feature has been used for music genre classification [28].