Let \(\{x_{N,l}(m)\}_{m=0}^{N-1}\) be a given (observed) discrete time signal, which is supposed to be the superposition of \(l\) sinusoidal waves. The problem addressed is to estimate the (unknown) frequencies of these waves. In other words, suppose that \(x_{N,l}(m)\) can be written on the form \[ x_{N,l}(m)= \sum_{j=-l}^ l \alpha_ j e^{i\omega_ j m}; \qquad 0\leq m<N, \] where \(\omega_ 0=0\), \(\alpha_ 0\geq 0\) and \(0<\omega_ j=- \omega_{-j}<\pi\), \(\alpha_ j= \overline{\alpha}_{-j}\) for \(1\leq j<N\), and estimate the frequencies \(\omega_ j\). The idea is to study the zeros \(z_ j (n,\psi_{N,l})\) of the Szegő polynomials \(\rho_ n (\psi_{N,l}; z)\) orthogonal on the unit circle with respect to the distribution function \(\psi_{N,l} (\theta)\) given by \[ \begin{alignedat}{2} \psi'_{N,l}(\theta) &= {1\over {2\pi}} \left| \sum_{m=0}^{N-1} x_{N,l}(m) e^{-im\theta} \right|^ 2 &\qquad &\text{if} \quad N<\infty\\ \psi_{\infty,l} (\theta) &= \sum_{j;\omega_ j\leq\theta} |\alpha_ j|^ 2 &\qquad &\text{if} \quad N=\infty.\end{alignedat} \] This procedure had been established previously for the case \(l<\infty\). In the present paper \(l=\infty\) is allowed under the additional condition that \[ \sum_{j=-l; j\neq -k}^ l\;\sum_{k=-l}^ l \left| \alpha_ j \alpha_ k \csc {{\omega_ j+\omega_ k} \over 2} \right|<\infty, \] which implies \(\sum_{j=0}^ l |\alpha|< \infty\). One cannot expect to determine infinitely many frequencies by a polynomial method, but the frequencies \(\omega_ j\) associated with relatively large amplitudes are approximated. It is also proved that \[ {\textstyle {1\over N}} \psi_{N,l} (\theta)\to{}^*\psi_{\infty,l} (\theta) \qquad \text{as} \quad N\to\infty \qquad \text{(weak star convergence)} \] when \(0<l\leq\infty\).