On the condition of four-parameter sine wave fitting

Matrix equations need to be solved in each round of an iterative algorithm for four-parameter sine wave fitting. The condition number (CN) of its coefficient matrix was studied approximately under a practical scenario (large sample size, and the frequency being well inside [0, Nyquist frequency]). Upon the first approximate level, secondary entries in the coefficient matrix are ignored. Thereafter, their contribution is examined by the matrix perturbation theory on the second approximate level. This study shows that, firstly, the CN does not depend on the offset. Secondly, the CN at the first approximate level only depends on the amplitude. Thirdly, the secondary entries modulate the CN weakly, and when the amplitude deviates away from the optimal value, this modulation is sinusoidal.