Spatio-temporally modulated impedance surfaces can be good candidates for generation of radiating waves with arbitrary eigenstates by breaking momentum and energy conservations. Here, we present a theoretical framework based on the holographic technique and generalized Floquet-wave expansion to analyze spatio-temporally modulated impedance surfaces. The holographic technique estimates the required impedance distribution to achieve the desired momentum. Injecting temporal modulation deviates the eigenvalues and changes the radiation frequency. Using the proposed analytical model, the eigenvalues can be calculated accurately in the presence of space and time modulations. Consequently, it is possible to predict the propagation mechanism of bounded and radiation states. It has been shown that, imposition of temporal modulation causes the Doppler-shift effect and nonreciprocal responses in the hologram. By plotting the antenna dispersion diagram, and observing the asymmetric displacement of dispersion curve due to temporal modulation, the system nonreciprocity can be verified. The beam scanning properties of these structures have also been investigated.