  Human hearing range significantly surpasses the typical neuronal spiking
frequency. Yet, neurons with their modest frequency range not only efficiently
receive and process multiple orders higher frequency signals, but also
demonstrate remarkable stability and adaptability to frequency variations in
brain functional connectivity. Ability to process signals beyond the
limitations of the receiver temporal or frequency (bandwidth) resolution is
highly desirable yet requires complex design architectures. Using the
FitzHugh-Nagumo model we reveal the harmonic fractal transformation of
frequency and bandwidth, which enables the Nyquist rate integer (for low
frequencies) and sub-integer (for high frequencies) multiplication. We also
demonstrate for the first time that noise shaping can be achieved in a simple
RLC-circuit without a requirement of a delay line. The discovered effect
presents a novel regeneration type - 4R: re-amplifying, re-shaping, re-timing,
and re-modulating and due to the fractal nature of transformation offers a
remarkable regenerative efficiency. The effect is a generalization of phase
locking to non-periodic encoded signals. The discovered physical mechanism
explains how using neuronal functionality one can receive and process signals
over an ultra-wide band (below or higher the spiking neuronal range by multiple
orders) and below the noise floor.
