A new approach to short-time harmonic analysis of tonal audio signals using harmonic sinusoidals

This paper presents a novel short-time frequency analysis algorithm, namely Instantaneous Harmonic Analysis (IHA), which can be used in Multiple Fundamental Frequency Estimation. Given a set of reference pitches, the objective of the algorithm is to transform the real-valued time-domain audio signal into a set of complex time-domain signals in such a way that the amplitude and phase of the resulting signals represent the amplitude and phase of the signal components with respect to the reference pitches. In the proposed algorithm, the instantaneous amplitude is identified as the presence of the pitch in time. The algorithm has been applied to three synthetic data sets for pureharmonic, one-overtone, and two-overtone data in a MIDI format and the results are reported here. To overcome the harmonic collision, a bottom of approach has been used for overtones elimination. A note event post-processing algorithm has also been developed for further analysis by representing the IHA output in the beat resolution.