Sparse Adaptive Representations for Musical Signals

Musical signals are, strictly speaking, acoustic signals where some aesthetically relevant information is conveyed through propagating pressure waves. Although the human auditory system exhibits a remarkable ability to interpret and understand these sound waves, these types of signals cannot be processed as such by computers. Obviously, the signals have to be converted into digital form, and this first implies sampling and quantization. In time-domain digital formats, such as the Pulse Code Modulation (PCM)—or newer formats such as one-bit oversampled bitstreams used in the Super Audio CD—audio signals can be stored, edited, and played back. However, many current signal processing techniques aim at extracting some musically relevant high-level information in (optimally) an unsupervised manner, and most of these are not directly applicable in the above-mentioned time domain. Among such semantic analysis tasks, let us mention segmentation, where ones wants to break down a complex sound into coherent sound objects; classification, where one wants to relate these sound objects to putative sound sources; and transcription, where one wants to retrieve the individual notes and their timings from the audio signals. For such algorithms, it is often desirable to transform the time-domain signals into other, better suited representations. Indeed, accord-ing to the Merrian-Webster dictionary, to ‘represent’ primarily means ‘to bring clearly before the mind’.