On the method of finding frequencies with large amplitudes (Q1921321)

Consider periodic signals of the form \[ x(m,I) = \sum_{j=-I}^I \alpha_j e^{i \omega_j m}, \qquad x(0, I) \neq 0, \] where \(\alpha_0 \geq 0\), \(\alpha_{-j} = \overline{\alpha_j}\), \(\omega_j = \omega_{-j}\) and \(0=\omega_0 < \omega_1 < \ldots < \omega_I < \pi\). The paper is concerned with the problem, how to determine the frequencies \( \omega_1, \ldots , \omega_I\) using the first \(N\) samples \(\{ x(m,I)\}_{m=0}^{N-1}\). A refined way of the Wiener-Levinson method is introduced in order to find the frequencies \(\omega_j\) with large amplitudes for small values of \(|j|\).