Interpolated DFT for $\sin^{\alpha}(x)$ Windows

Abstract

This paper describes interpolated discrete Fourier transform (IpDFT) for parameter estimation of sinusoidal and damped sinusoidal signals analyzed with a sinα(x) window. For α = 0,2,4,...sinα(x) windows are Rife-Vincent class I (RVI) windows, for which IpDFT algorithms are known. We present a new IpDFTs for α = 1,3,5,.... The bias-variance trade-off of the proposed IpDFT fits between results offered by RVI windows, e.g., for α = 1, we get higher noise immunity than Hann (RVI order 1, α = 2) window and lower bias than rectangular (RVI order 0, α = 0) window.