Embodiments of the present invention are low cost, robust, broadband, optimum, high precision methods and apparatus of processing pulsed, transient, non-cooperative, non-reproducible, complex, or simultaneous signals based on correlation measurements utilizing optical RF signal train generators. An embodiment of the inventive apparatus comprises: (a) a signal receiving apparatus which receives one or more signals, and outputs the signals; (b) a replica generation apparatus, which comprises one or more RF signal train generators, accepts signals from the receiving apparatus as inputs, and outputs trains of replica pairs, where relative separations between two members in the replica pairs are same or different; and (c) an integration apparatus which performs Doppler, self, or mutual (cross) correlation operations on the replica pairs at RF or optical level. The apparatus of present invention advance interferoceivers of prior art, and overcome deficiencies of radar receivers, channelized receivers, electronic warfare receivers, spectrum analyzers, sampling oscilloscopes, and many others.