Nonlinear Dynamics from Infinite Impulse Response Matched Filters
Standard methods of communication theory are used to derive optimal waveforms for transmitting information through noise using infinite impulse response matched filters as receivers. In two examples, the derived optimal communication waveforms are chaotic. Extrapolating from these simple examples, we posit that the optimal communication waveform for any stable infinite impulse response filter can similarly be chaotic. This conjecture implies the phenomena of nonlinear dynamics and chaos are fundamental and essential to a full understanding of modern communication theory.