Adaptive frequency estimation based on normal realizations and its application in speech processing

We investigate the problem of direct frequency estimation. A new adaptive algorithm is proposed based on G. Li´s earlier work (see IEEE Trans. on Sig. Processing, vol.45, no.8, p.2001-9, 1997), where the constrained pole-zero notch filter was cascaded and each stage was implemented with controllable realization. It is well known that the performance of adaptive filters is strongly related to how the filters are parametrized and implemented. The normal based realizations have some nice numerical properties. In the proposed algorithm, each subfilter is parametrized with its notching frequency and implemented with a normal realization. Compared with Li´s earlier structure, this one makes the algorithm more robust, such that the stability can be ensured automatically no matter whether the algorithm is implemented with or without infinite precision. Simulations show that the adaptive algorithm with the proposed structure also has better convergence behavior. Application of this algorithm to speech processing is also discussed.