Instantaneous frequency and short term fourier transforms: application to piano sounds

For more than 30 years and until nowadays, development of a system reproducing the functioning of human hearing has remained an aim difficult to reach. Recent methods for identification of the fundamental frequency of musical sounds obtain good results using information about the temporal evolution of the amplitude and frequency of individual sound partials. Piano sounds and polyphonic sounds, which can have several partials that are closely spaced in the frequency domain, have not been extensively tested by these procedures. In this paper, the Instantaneous Frequency (IF), as defined by the Hilbert transform, is used to obtain the frequency variations of piano sounds partials. The result implies that, for these sounds, the IF may contain modulations resulting in the separation of an apparent single sinusoid signal into two or more sinusoidal components at various times in the analysis process, which makes it impossible to use the temporal evolution of the frequency of partials for the procedure of note identification. The separation phenomenon also appears when the short term Fourier transform is used and can induce the detection of short-lived parasitic spectral peaks that must be taken into account by any note identification procedure based on the use of spectral information.