Time-variant least squares harmonic modeling

An algorithm for harmonic decomposition of time-variant signals is derived from a least squares harmonic (LSH) technique. The estimates of harmonic amplitudes and phases are formulated as the solution of a set of linear equations which minimizing mean square error; the signal frequency is modeled by a linear or quadratic polynomial and obtained via a local search over polynomial coefficients. An initial estimate of signal frequency is necessary to reduce computation time. This method is capable of producing accurate and robust harmonic estimation in low SNR situations. We show applicability to high accuracy speech pitch and heart sound beat epoch estimation.