Sinewave analysis/synthesis has long been an important tool for audio analysis, modification and synthesis [1]. The recently introduced Fan-Chirp Transform (FChT) [2,3] has been shown to improve the fidelity of sinewave parameter estimates for a harmonic audio signal with rapid frequency modulation [4]. A fast version of the FChT [3] reduces computation but this algorithm presents two factors that affect sinewave parameter estimation. The phase of the fast FChT does not match the phase of the original continuous-time transform and this interferes with the estimation of sinewave phases. Also, the fast FChT requires an interpolation of the input signal and the choice of interpolator affects the speed of the transform and accuracy of the estimated sinewave parameters. In this paper we demonstrate how to modify the phase of the fast FChT such that it can be used to estimate sinewave phases, and we explore the use of various interpolators demonstrating the tradeoff between transform speed and sinewave parameter accuracy.