An extension of the fast algorithm for linear phase system identification

A fast (computationally efficient) least squares algorithm to fit a Mth order linear phase (symmetric) FIR system to an input/output sequence was presented in reference [1]. This algorithm solved the normal equations associated with the least squares procedure with a number of computations proportional to M
²
, rather than M
³
as required for general purpose linear equation algorithms. The linear phase system identification problem occurs in certain signal processing applications where no phase distortion is a requirement. The fast algorithm is possible due to the near-to-Toeplitz plus-Hankel-property of the normal equation matrix. The algorithm reported in [1] required 2NM + 24M
²
operations, where N is the number of data samples. This paper describes some additional properties that further reduces this complexity to 2NM + 18M
²
. This results in a computational savings of 15% to 20% for typical values of N and M.