Spectral Modelling for Transformation and Separation of Audio Signals

The Short-Time Fourier Transform is still one of the most prominent time-frequency analysis techniques in many fields, due to its intuitive nature and computationally-optimised basis functions. Nevertheless, it is far from being the ultimate solution as it is plagued with a variety of assumptions and user-specific design choices, which result in a number of compromises. Numerous attempts have been made to circumvent its inevitable internal deficiencies, which include fixed time-frequency resolutions, static sample points, and highly biased outputs. However, its most important assumption, stationarity, is yet to be dealt with effectively.
A new concept is proposed, which attempts to improve the credibility of the STFT results by allowing a certain degree of deviation from stationarity to be incorporated into the analysis. This novel approach utilises an ensemble of estimates instead of a single estimation in order to investigate the short-time phase behaviour of every frequency bin. The outcome is the definition of a quality measure, phase stability, that discriminates the "structured" from the "artefact" frequency components. This quality measure is then used in the framework of source separation as a single application example where it is possible to investigate its potential on the performance of the algorithm. Specifically, it was used in the spectral peak picking step of a numerical model-based source separation algorithm. It was found that the phase stability quality measure acts as an effective data reduction tool, which qualifies it as a more appropriate thresholding technique than the conventional methods.
Based on this example, it is anticipated that this new method has great potential. Its ability to discriminate between "structured" and "noise" or edge effect/"artefacts" qualifies it as a promising new tool that can be added in the arsenal of the STFT modifications and used in the development of a hybrid super-STFT.