A method is described which applies the linear prediction directly to fundamental frequency analysis of the speech wave. Most methods hitherto proposed use the linear prediction indirectly estimating the spectral envelop. With an appropriate band-width and a number of terms, the linear prediction can be shown to estimate the spectral fine structure. The fundamental component is included among the roots of its characteristic equation. This method does not use explicit peak-picking or interpolation. Experimentally, the bandwidth is chosen between 300 - 900 Hz, and the number of coefficients 4 - 8. The method gives very accurate results without much computation, and is possibly applicable to coding the base-band of a vocoder.