Effect of the Sampling Time on the Accuracy of Estimating the Frequencies of Multiple Sinusoids

The accuracy of the estimates of the frequencies of multiple sinusoids in noise depends on many factors. Among these factors are the signal to noise ratio, the estimation technique, the number of sinusoids and their relative values. An estimation technique was suggested recently that yields the required frequencies as the generalized eigenvalues of two matrices formed from samples of the sinusoids and a filtered signal of these sinusoids. It was found that the sampling time has a profound effect on the accuracy of the resulting estimates. Recent interest in eigenstructure techniques in engineering applications led to increasing interest in the mathematical literature addressing the generalized eigenproblem. Recent studies exposed the relation between the condition of the generalized eigenproblem and the condition of a corresponding Vandermonde matrix. In this paper it is shown that the condition of the Vandermonde matrix can be influenced by the choice of the sampling time, consequently improving the generalized eigenproblem condition and making the frequency estimation technique more immune to noise