Detecting and estimating multiple fundamental frequencies is essential for automatic/semi-automatic music transcription, conversion to MIDI signals, music information retrieval, etc. However, fundamental frequency can not easily be detected from a multi-pitch audio signals such as multitone or polyphonic music, mainly due to spectral overlap, poor frequency resolution and widened spectrum in short-time analysis, etc. Conventionally, various approaches concerning the multi-pitch detection/estimation problem have been attempted[2,3,4,5]. Goto[6] proposed a predominant fundamental frequency estimation by modeling a multi-pitch spectrum itself with Gaussian-mixture-harmonic-structure models. The relative dominance of the fundamental frequencies are estimated by the weight parameter estimation of the harmonic structure models using the EM algorithm. Kameoka et al.[7,8] proposed a robust multi-pitch estimation derived from fuzzy clustering principle similar to Goto's approach but different in respect that the parameters to be estimated are the means of Gaussians. AIC is effectively used in this method for estimating the number of simultaneous sounds and also for taking care of double/half pitch errors. These two methods are commonly based on parameter optimization by iterative computation that occasionally brings unpredictable mistakes depending on initial values.
Our objective is to provide a visualization technique representing fundamental frequency components by suppressing harmonic components in the given spectrum and produce a ``piano-roll'' display similar to that of MIDI signal display. The motivation of our approach is different from those of most conventional methods that give only the most likely solutions to the multi-pitch detection/estimation problem, in which errors/mistakes are necessarily involved partly due to local optimum problems. Instead, the visualization approach gives a global image with ``soft decision'' of fundamental frequencies of the signal. The result can be used in automatic or semi-automatic transcription of music, conversion of music signal into MIDI format, and efficient initial value estimation for more precise multipitch analysis[7,8].