A real-time spatial–temporal processor based on cascaded nonlinearities converts space-domain images to time-domain waveforms by the interaction of spectrally decomposed ultrashort pulses and spatially Fourier-transformed images carried by quasi-monochromatic light waves. We use four-wave mixing, achieved by cascaded second-order nonlinearities with type II noncollinear phase matching, for femtosecond-rate processing. We present a detailed analysis of the nonlinear mixing process with waves containing wide temporal and angular bandwidths. The wide bandwidths give rise to phase-mismatch terms in each process of the cascade. We define a complex spatial–temporal filter to characterize the effects of the phase-mismatch terms, modeling the deviations from the ideal system response. New experimental results that support our findings are presented.