Low-level Descriptors
As mentioned before, low level descriptors are closely related to the signal itself. We can distinguish at least three levels of extraction granularity from the signal: at any point of the signal, in small arbitrary regions (i.e. frames) and in longer pre-segmented regions.
The set of features that can be extracted at any point in the signal are called instantaneous descriptors. In the case of a time domain representation, most of the useful instantaneous values that can be computed are related to the amplitude or energy of the signal.
If we are dealing with a frequency-domain representation many spectrum-related instantaneous features, such as the spectral centroid or the spectral tilt, can be computed on a given point. To be more precise, one should consider these descriptors as nearly instantaneous as they are not associated to a point in time of the signal but rather to a small region or frame.
An important step towards a musically useful parameterization is the segmentation of a sound into regions that are homogeneous in terms of a set of sound attributes. The goal is to identify regions that, using the signal properties, can then be classified in terms of their content. This way we can identify and extract region attributes that will give higher-level control over the sound.
A useful segmentation process applied to a monophonic source divides a melody into notes and silences and then each note into an attack, a steady state and a release regions. Attack and release regions are identified by the way the instantaneous attributes change in time and the steady state regions are detected by the stability of these same attributes. Global attributes that can characterize attacks and releases refer to the average variation of each of the instantaneous attributes, such as average fundamental frequency variation, average amplitude variation, or average spectral shape change. In the steady state regions, it is meaningful to extract the average of each of the instantaneous attributes and measure other global attributes such as time-varying rate and depth of vibrato [Gómez et al., 2003a].
Once a given sound has been segmented into regions we can study and extract the attributes that describe each one. Most of the interesting attributes are simply the mean and variance of each of the frame attributes for the whole region. For example, we can compute the mean and variance for the amplitude of sinusoidal and residual components, the fundamental frequency, the spectral shape of sinusoidal and residual components, or the spectral tilt.
Region attributes can be extracted from the frame attributes in the same way that the frame attributes are extracted from the frame data. The result of the extraction of the frame and region attributes is a hierarchical multi-level data structure where each level represents a different sound abstraction.
From several sound representations it is possible to extract the type of attributes mentioned above. The critical issue is how to extract them in order to minimize interferences, thus obtaining, as much as possible, meaningful high-level attributes free of correlations.
Up until this point, we have extracted and computed features that are directly related to the signal-domain characteristics of the sound and, although they may have a perceptual meaning, they are not taking into account the importance of the listeners perceptual filter.
In that sense, for example, it is well known that the amplitude of the sound is not directly related to the sensation of loudness produced on the listener, not even in a logarithmic scale (see [Moore et al., 1997]). [Fletcher and Munson, 1933] established a set of equal-loudness curves called isophones. The main characteristic of these curves is that the relation between a logarithmic physical measure and its psychoacoustical counterpart is a frequency dependant function. Although this curves have proven only valid for the stable part of pure sinus (more than 500 ms), they have been used as a quite robust approximation for measuring loudness of complex mixtures [Pfeiffer, 1999].
Any audio signal can be represented as a time-domain signal or as its spectral transform, and following this same idea we can separate low-level descriptors into two categories: temporal and spectral descriptors.
Temporal descriptors can be immediately computed from the actual signal or may require a previous adaptation stage in order to extract the amplitude or energy envelope of the signal, thus only taking into account the overall behavior of the signal and not its short-time variations. Examples of temporal descriptors are attack time, temporal centroid, zero-crossing rate, etc...
Many other useful descriptors can be extracted from the spectrum of an audio signal. These descriptors can be mapped to higher-level attributes. As a matter of fact, of the basic dimensions of a sound, two of them (pitch and brightness) are more easily mapped to frequency domain descriptors and a third one (timbre) is also very closely related to the spectral characteristics of a sound. A previous analysis step needs to be accomplished in order to extract the main spectral features. Descriptors directly derived from the spectrum are, for example: spectral envelope, power spectrum, spectral amplitude, spectral centroid, spectral tilt, spectral irregularity, spectral shape, spectral spread; derived from the spectral peaks: number of peaks, peak frequencies, peak magnitudes, peak phases, sinusoidality; derived from a fundamental detection: fundamental frequency, harmonic deviation; etc...