A numerically-stable sliding-window estimator and its application to adaptive filters

While it is possible to implement the sliding discrete Fourier transform (DFT) recursively, numerical errors accumulate in the resulting outputs. This paper presents a recursive system whose output at every Lth sample time is equivalent to that of the sliding DFT and whose numerical errors do not grow with time. We provide a statistical analysis of the numerical performance of the proposed technique, showing that it outperforms a similar approximate method employing an exponentially-decaying window. When applied to sliding-window-covariance RLS adaptive filters, the technique mitigates this system's error accumulation without any significant increase in complexity. An extension of the method to the sliding discrete cosine transform (DCT) is also provided.