Fast adaptive least squares algorithms for power spectral estimation

Power spectrum estimation is of great importance in various applications of signal processing, such as geophysics and communications. In this paper two new fast algorithms are presented that adaptively compute a least squares estimate of the power spectrum of a time series. This is achieved by modeling the input as an AR signal of order m and simultaneous minimization of the sum of the forward and backward prediction error energies. The first algorithm is of the 0 (m²) type, and the second of 0(m) requiring 9m multiplications and additions.