Piano Fundamental Frequency Estimation Algorithm Based on Weighted Least Square Method

Fundamental frequency estimation(FFE) has been studied for many years, and current techniques are still not accurate and robust. Because of the fundamental frequency losing, the harmonic losing and the inharmonicity of piano sound, these FFE methods are invalid generally. The mean square error of the harmonic frequency based on quadratic interpolation of FFT is discussed, and the influence of other harmonic sidelobe on the harmonic measurement with the different length Hanning, Hamming, Chebyshev and Blackmanharris windows is analyzed. A FFE algorithm using weighted least square method is derived. The simulation experiment shows that the method is feasible, and the relative error is about 10e-5.

[1]  Mototsugu Abe,et al.  Design Criteria for Simple Sinusoidal Parameter Estimation Based on Quadratic Interpolation of FFT Magnitude Peaks , 2004 .

[2]  Jia Xin-le,et al.  Accuracy Analysis of Frequency Estimation of Sinusoid Based on Interpolated FFT , 2004 .

[3]  Hideki Kawahara,et al.  YIN, a fundamental frequency estimator for speech and music. , 2002, The Journal of the Acoustical Society of America.

[4]  Christopher Raphael,et al.  Automatic Transcription of Piano Music , 2002, ISMIR.

[5]  S. Hamid Nawab,et al.  Improved musical pitch tracking using principal decomposition analysis , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[6]  Xavier Rodet,et al.  Fundamental frequency estimation and tracking using maximum likelihood harmonic matching and HMMs , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[7]  Xavier Rodet,et al.  Estimation of fundamental frequency of musical sound signals , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[8]  A. P. Speiser,et al.  The Physics of Musical Instruments. Von Neville H. Fletcher und Thomas D. Rossing, Springer-Verlag, Berlin, 1991, 620 Seiten, geb., DM 148,– , 1991 .

[9]  B. Kedem,et al.  Spectral analysis and discrimination by zero-crossings , 1986, Proceedings of the IEEE.

[10]  B. Galler,et al.  Predicting musical pitch from component frequency ratios , 1979 .

[11]  V. Jain,et al.  High-Accuracy Analog Measurements via Interpolated FFT , 1979, IEEE Transactions on Instrumentation and Measurement.

[12]  D. C. Rife,et al.  Use of the discrete fourier transform in the measurement of frequencies and levels of tones , 1970, Bell Syst. Tech. J..