Klapuri A., Multiple Fundamental Frequency Estimation Based on
Harmonicity and Spectral Smoothness, IEEE Transactions on Speech and
Audio Processing, vol.. 11, n.. 6, pp. 804-816, 2003
Abstract
A new method for estimating the fundamental
frequencies of concurrent musical sounds is described. The
method is based on an iterative approach, where the fundamental
frequency of the most prominent sound is estimated, the sound
is subtracted from the mixture, and the process is repeated for
the residual signal. For the estimation stage, an algorithm is proposed
which utilizes the frequency relationships of simultaneous
spectral components, without assuming ideal harmonicity. For the
subtraction stage, the spectral smoothness principle is proposed
as an efficient new mechanism in estimating the spectral envelopes
of detected sounds. With these techniques, multiple fundamental
frequency estimation can be performed quite accurately in a
single time frame, without the use of long-term temporal features.
The experimental data comprised recorded samples of 30 musical
instruments from four different sources. Multiple fundamental
frequency estimation was performed for random sound source and
pitch combinations. Error rates for mixtures ranging from one to
six simultaneous sounds were 1.8%, 3.9%, 6.3%, 9.9%, 14%, and
18%, respectively. In musical interval and chord identification
tasks, the algorithm outperformed the average of ten trained
musicians. The method works robustly in noise, and is able to
handle sounds that exhibit inharmonicities. The inharmonicity
factor and spectral envelope of each sound is estimated along with
the fundamental frequency.
Index Terms
Acoustic signal analysis, fundamental frequency
estimation, music, music transcription, pitch perception.