We have developed new measurement methods for the dynamic light scattering in a periodically stationary system such as the quasi-elastic light scattering with the sinusoidal(ac) electric field (QELS-SEF). Whereas the usual dynamic light scattering is measured in the stationary system, the scattered light intensity in QELS-SEF obeys a nonstationary stochastic process, more specifically, a periodically stationary one. Hence, the autocorrelation function or the power spectrum in QELS-SEF is a bivariable function of two independent times or frequencies, which cannot be measured by the conventional correlator or spectrum analyzer. We have designed a new kind of spectrum analyzer for QELS-SEF and obtained two-dimensional power spectrum of QELS-SEF by use of an extended Wiener-Khinchin theorem. Furthermore, the data analysis formula for the two-dimensional spectra is calculated to evaluate the complex electrophoretic mobility mu* and the apparent diffusion constant D-app of polyions from the two-dimensional power spectra. They are in good agreement with the experimental results of QELS-SEF for a polystyrene latex solution.