The invariant-subspace based (ISP) system identification method is developed when the excitation signal is periodic and the measured data are obtained from irregular samplings. With the ISP method, frequency response data are obtained using least-square estimators, which reduces to discrete Fourier transformation (DFT) if the sampling is periodic. Then, with a careful use of the statistics of the sampled data, consistency of the identified model is established when the sampling rates at the input and output channels are nonuniform, asynchronous, and slow. It is further revealed that, if the noise signals at the input and output channels are uncorrelated with respect to the sampling moments, their estimates in the frequency domain are asymptotically uncorrelated. In that case, the proposed algorithms asymptotically reduce to the existing frequency-domain identification algorithms.