Performance Analysis of an Inverse Notch Filter and Its Application to <i>F<sub>0</sub></i> Estimation
- 1 Graduate School of Engineering Science, Osaka University, Osaka, Japan
- 2 Graduate School of Engineering Science, Osaka University, Osaka, Japan
- 3 Graduate School of Engineering Science, Osaka University, Osaka, Japan
Abstract
In this paper, we analyze an inverse notch filter and present its application to F 0 (fundamental frequency) estimation. The inverse notch filter is a narrow band pass filter and it has an infinite impulse response. We derive the explicit forms for the impulse response and the sum of squared impulse response. Based on the analysis result, we derive a normalized inverse notch filter whose pass band area is identical to unit. As an application of the normalized inverse notch filter, we propose an F 0 estimation method for a musical sound. The F 0 estimation method is achieved by connecting the normalized inverse notch filters in parallel. Estimation results show that the proposed F 0 estimation method effectively detects F 0 s for piano sounds in a mid-range.
- A. Nehorai, “A Minimal Parameter Adaptive Notch Filter with Constrained Poles and Zeros,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 33, No. 4, 1985, pp. 983-996. doi:10.1109/TASSP.1985.1164643
- H. C. Chong and U. L. Sang, “Adaptive Line Enhancement by Using an IIR Lattice Notch Filter,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 37, No. 4, 1989, pp. 585-589. doi:10.1109/29.17543
- C. C. Tseng and S. C. Pei, “IIR Multiple Notch Filter Design Base on Allpass Filter,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 44, No. 2, 1997, pp. 133-136.
- S. C. Pei, W. S. Lu and C. C. Tseng, “Analytical TwoDimensional IIR Notch Filter Design Using Outer Product Expansion,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 44, No. 9, 1997, pp. 765-768.
- Y. V. Joshi and S. C. D. Roy, “Design of IIR Multiple Notch Filters Based on All-Pass Filters,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 46, No. 2, 1999, pp. 134-138.
- M. Goto, “A Real-Time Music-Scene-Description System: Predominant-F0 Estimation for Detecting Melody and Bass Lines in Real-World Audio Signals,” Speech Communication, Vol. 43, No. 4, 2004, pp. 311-329. doi:10.1016/j.specom.2004.07.001
- V. DeBrunner, “An Adaptive, High-Order, Notch Filter Using All Pass Sections,” IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 3, Seattle, 12-15 May 1998, pp. 1477-1480.
- Y. Xiao, “A New Efficient Narrowband Active Noise Control System and Its Performance Analysis,” IEEE Transactions on Audio, Speech, and Language Processing, Vol. 19, No. 7, 2011, pp. 1865-1874. doi:10.1109/TASL.2010.2101598