Non-stationary sinusoidal analysis

Signal analysis is a ground-level basis of many scientific applications. Since computers have become powerful enough to analyze/synthesize sound in real-time, field has received even more attention. Most of computer sound applications use Fourier analysis in one form or another. It is used for as simple cases as visualizing sound, extracting general sound features or providing basis for accurate sound parameterization techniques. Its popularity lies in the fact, that Fourier transform provides very human readable and sonically meaningful parameterization. With discovery of Fast Fourier Transform in 1965 and ideas like phase vocoding eventually led to development of Spectral Modeling Synthesis. This synthesis method essentially synthesizes sound from a spectrum, a word widely used to denote Fourier transform. Constructing a reasonably good spectrum from scratch can be a painstakingly long lasting task, so some kind of templates should be used. Such templates can be extracted from sounds of instruments. Such procedure can result in very naturally sounding synthetic sounds. Of course, a high quality analysis is a must, as the most interesting instruments tend to contain numerous details in form of subtle frequency and amplitude modulations, giving it its distinct character, recognized by producers and music lovers alike. To present day, sounds are analyzed by segmenting it into smaller pieces and applying analysis methods frame by frame. Such method is very practical, as it can be used in real-time manner, but forces one to make a trade-off. Most analysis methods assume, that sound is completely stationary within one frame. In case that signal does not posses such property, smaller frames are taken. Clearly, frame cannot be made arbitrarily small for many different reasons, so a need of non-stationary signal analysis technique was obvious. When analyzing sound with intent to use it for spectral modeling synthesizer specifically, a specific form of non-stationary signal analysis is used: non-stationary sinusoidal analysis. In essence, such analysis should be able to detect fast frequency and amplitude changes of sinusoids, even if such changes occur inside a analysis frame, even if there is more sinusoids relatively close to each other in frequency and even in presence of noise