There have been numerous recent strides at making sinewave analysis consistent with time-varying sinewave models. This is particularly important in high-frequency speech regions where harmonic frequency modulation (FM) can be significant. One notable approach is through the Fan Chirp transform that provides a set of FM-sinewave basis functions consistent with harmonic FM. In this paper, we develop a complete sinewave analysis/synthesis system using the Fan Chirp transform. With this system we are able to obtain more accurate sinewave frequencies and phases, thus creating more accurate frequency tracks, in contrast to a system derived from the short-time Fourier transform, particularly for high-frequency regions of large-bandwidth analysis. With synthesis, we show an improvement in segmental signal-to-noise ratio with respect to waveform matching with the largest gains during rapid pitch dynamics.