This paper describes a new method of estimating the fundamental frequency of speech signals using an adaptive Fourier analysis (AFA) algorithm based on the presumption of signal parameters using a nonlinear observer. The recursive presumption of signal parameters such as fundamental frequency can be effectively implemented by using the proposed AFA algorithm. Nonlinear observers can be used to measure nonlinear parameters which are included in observed signals. Recursive estimation procedures make it possible to follow the slow changes of signal parameters to be measured. In real-time signal analysis, the recursive algorithm is preferred to the conventional Fourier transformation because of this property. The AFA algorithm, which is based on the recursive discrete Fourier transform (RDFT), is a recursive algorithm for the simultaneous estimation of the Fourier coefficients and instantaneous fundamental frequency of speech signals. This AFA algorithm is applied to speech signals with an arbitrary length of the transform window. Further efforts are required for better convergence speed of the proposed algorithm, but this method is mostly capable of adapting and tracking nonlinear signals such as speech sound.