A new identification algorithm which identifies low complexity models of infinite-dimensional systems from equidistant frequency-response data is presented. The new algorithm is a combination of the Fourier transform technique with the recent subspace techniques. Given noise-free data, finite-dimensional systems are exactly retrieved by the algorithm. When noise is present, it is shown that identified models strongly converge to the balanced truncation of the identified system if the measurement errors are covariance bounded. Several conditions are derived on consistency, illustrating the trade-offs in the selection of certain parameters of the algorithm. Two examples are presented which clearly illustrate the good performance of the algorithm.