Waves are fundamental. In our view, waves in the brain may constitute and drive organized neural activity patterns on individual neural and population levels. Their interactions follow basic physical principles. Taking a comprehensive, temporal and spatiotemporal perspective, we endeavor to explain multiple brain functions and behaviors with a unified mechanistic approach. Starting with neural architectures, traveling waves, and spikes as the basic signals of the system, our multidisciplinary theory proposes that precise temporal phase-locking codes, spike coincidences, phase relationships, recurrent networks, temporal and spatiotemporal population patterns, pattern correlations, their interactions, synchronizations and couplings play an essential role in determining brain dynamics at multiple processing scales. Analogously to optical holography, it posits that traveling brain waves convey spike timing information, interact to form distinctive time/phase interference patterns and spatially distribute these widely. These in turn can interact with other traveling waves producing yet new spike patterns. Traveling waves also serve to selectively reactivate/refresh existing patterns. Spatially distributed temporal spike patterns and representations derived from these, are used to code, process, synchronize, integrate, and decode objects (e.g., sensorimotor events, concepts, etc.). We apply established physical principles (e.g., wave dynamics, holography) and signal processing principles (e.g., linear additive operations, and nonlinear, multiplicative frequency mixing). This theory proposes that oscillations may serve as signal carriers for communications in transmitting progressively processed signals through an emergent cascade of neuron mixing stages. Such cascades closely correspond to intermediate frequency (IF) processing stages in broadly used radio communications, specifically superheterodyned Single Sideband Suppressed Carrier (SSBSC = SSB) communications technology. This is illustrated with a numerical speech/language hierarchy oscillatory cascade model. This model correlates signal processing stages with both canonical oscillation bands and associated cognitive stages. Plausible biophysical mechanisms are proposed to realize these processes. Many neurophysiological observations consistent with these proposed mechanisms are referenced. This proposal is novel in suggesting conceptual integrations and coordinations of multiple disciplines that mechanistically trace informational neural signals from inception to conception. Some suggestions for empirically testing these hypotheses are presented.