Performance analyses of Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform (CNFT)

Fourier analysis of sinusoidal and/or quasi-periodic signals in additive no ise has been used in various fields. So far, many analysis algorithms inclu ding the well-known DFT have been developed. In particular, many adaptive a lgorithms have been proposed to handle non-stationary signals whose discret e Fourier coefficient (DFCs) are time-varying. Notch Fourier Transform (NFT ) and Constrained Notch Fourier Transform(CNFT) proposed by Tadokoro et al. and Kilani et al., respectively, are two of them, which are implemented by filter banks and estimate the DFCs via simple sliding algorithms of their own. This paper presents, for the first time, statistical performance analy ses of the NFT: and the CNFT. Estimation biases and mean square errors (MSE s) of their sliding algorithms will be derived in closed Form. As a result, it is revealed that both algorithms are unbiased, and their estimation MSE s are related to the signal frequencies, the additive noise variance and or ders of comb filters used in their filter banks. Extensive simulations are performed to confirm the analytical findings.