Coefficient-constrained lattice structures for retrieving single-tone harmonic signals

Abstract

Two modified lattice structures for retrieving a real, single-frequency harmonic signal from noisy data samples is presented. The first lattice structure comprises a two-stage cascaded lattice filter with the value of the second reflection coefficient constrained to unity. The first reflection coefficient, from which the sinusoidal frequency is estimated, is obtained by a procedure similar to that of Burg's method. In the noiseless case, this filter structure is able to compute exactly the sinusoidal frequency regardless of the initial phase or data record length. With the presence of white noise, however, it will yield a biased frequency estimate. To remedy this problem, a second lattice structure is proposed which imposes a unit-norm constraint on the resulting prediction error filter coefficients before minimising the resulting forward and backward prediction errors. It is shown that theoretically, even with the presence of white noise, this second lattice structure still yields unbiased estimates. A statistical performance analysis of these frequency estimation methods is derived and compared with simulation results.