Reconstruction of undersampled periodic signals of unknown period is an important signal processing operation. It is especially difficult operation when the sequences of samples are short and no information on the inter-sequence time distances is given. For such a case, there exist some algorithms that allow for approximation of the sampled signal. However, these algorithms require either bandlimitedness of the signal, or noiseless samples. In this paper, we propose a novel algorithm which does not require the signal to be bandlimited and it can cope with additive noise in the samples. The algorithm is illustrated and validated with real data.