In this paper, the results concerning unfalsified model parametrization are extended to the case where identification noises are magnitude bounded in the frequency domain. It is shown that while every unfalsified model can still be represented by a linear fractional transformation of a block diagonal norm bounded transfer function matrix, the dimensions of the involved matrix valued transfer functions are of the order of the identification experiment data length. Moreover, the verification of the parametrization condition only requires computing the maximal singular values of two constant matrices. These results are established on the basis of a relation between a lower-triangular Toeplitz matrix and the discrete Fourier transformation of its first column elements. However, an analysis shows that the parametrization condition can be satisfied only when the noise level is very low. This implies that the proposed least-squares minimization-based algorithms are not very appropriate in model set identification.