An analysis by synthesis procedure based on the SVN methodology is proposed. Using this procedure, a new criterion for detecting the number of sinusoidal signals in the presence of noise is defined. Consecutive reconstructions are performed and the resulting error power is compared to the noise variance in order to get the best approximation of the original noncorrupted signal. The number of the singular values corresponding to a reconstruction error power as close as possible to the noise variance gives the parsimonious order. The existence of such a criterion is important both for high quality reconstruction and spectral analysis. Various spectral estimation techniques used on a reconstructed signalgive the possibility to retrieve harmonics in highly noisy environment with very short data lengths.