ESTIMATION OF MULTIPLE SINUSOIDAL FREQUENCIES USING TRUNCATED LEAST-SQUARES METHODS

Abstract

Various SVD-based methods have been shown effective for resolving closely spaced frequencies. However, the massive computations required by SVD makes it unsuitable for real-time applications. To reduce the computational complexity, three truncated QR methods are proposed: 1) truncated QR without column pivoting (TQR); 2) truncated QR with reordered columns (TQRR); and 3) truncated QR with column pivoting (TQRP). It is demonstrated that many of the benefits of the SVD-based methods are achievable under the truncated QR methods with much lower computational cost. Based on the forward-backward linear prediction model, computer simulations and comparisons are provided for different truncation methods under various SNR's. Comparisons of asymptotic performance with large data samples are also given.