Constrained lattice structures for harmonic retrieval

This paper presents two novel Lattice structures for retrieving single sinusoidal signal from noisy data samples. Our approach is to make use of a two-stage cascaded lattice filter with the second reflection coefficient being set equal to unity. The first reflection coefficient, from which the sinusoidal frequency is estimated, is obtained by minimizing the sum of the "forward" and "backward" prediction error of the output in a procedure similar to that of the Burg\´s method. At noiseless case, such a structure is able to compute the exact sinusoidal frequency regardless of the initial phase or data record length. With the presence of white noise, however, such an approach will yield biased frequency estimate. For this, we propose a further modification by including a normalization factor at the output, then minimize the resulting forward and backward prediction errors. It is shown that with ideal white noise, this second lattice structure will give unbiased frequency estimate.