Performance Analysis of an Inverse Notch Filter and Its Application to F0 Estimation

In this paper, we analyze an inverse notch filter and present its application to F0 (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 F0 estimation method for a musical sound. The F0 estimation method is achieved by connecting the normal-ized inverse notch filters in parallel. Estimation results show that the proposed F0 estimation method effectively detects F0s for piano sounds in a mid-range