Applications of truncated QR methods to sinusoidal frequency estimation

Three truncated QR methods are proposed for sinusoidal frequency estimation: (1) truncated QR without column pivoting (TQR); (2) truncated QR with pre-ordered columns, (TQRR); and (3) truncated QR with column pivoting (TQRP). It is demonstrated that the benefit of truncated singular value decomposition (TSVD) for high-frequency resolution is achievable under the truncated QR approach with much lower computational cost. Other attractive features of these methods include the ease of updating, which is difficult for the SVD method, and numerical stability. Thus, the TQR methods offer efficient ways for identifying sinusoidals closely clustered in frequencies under stationary and nonstationary conditions. Based on the forward-backward linear prediction model, computer simulations and comparisons are provided for different truncation methods under various signal-to-noise ratios