Fast orthogonalization algorithm and parallel architecture for AR spectral estimation based on forward-backward linear prediction

Truncated QR methods have been shown to be comparable to SVD-based methods for the sinusoidal frequency estimation based on the forward-backward linear prediction (FBLP) model. However, without exploiting the special structure of the FBLP matrix, the QR decomposition (QRD) of the FBLP matrix has a computational complexity on the order of 2(6m-n)n²/3+O(n ²) for a 2m×n FBLP matrix. A fast algorithm to perform the QRD of the FBLP matrix by exploiting its special Toeplitz-Hankel form is proposed. The computational complexity is reduced to 10n²+4mn+O(n). The fast algorithm can also be easily implemented by a linear systolic array, reducing the number of time steps required to 2m+5n-4