The mutual time—Frequency content of two signals

Two independent, ongoing signals are shown to require four dimensions (4D) to describe the ongoing relationships among their times and frequencies. We derive a large number of suitable 4D functions for this purpose, show what each displays best, and show explicit interrelationships among them. The approach of studying two signals using their mutual 4D information pattern rather than by comparing their independent 2D patterns (e.g., Wigner patterns or ambiguity plots) offers a new and promising approach to a common and important problem. Because of symmetry, we can often show the 4D signal in 2D in a manner compatible with coherent optical real time display.