Prediction of spectral shifts proportional to source distances by time-varying frequency or wavelength selection

TL;DR

This paper proposes a method to predict spectral shifts proportional to source distances using time-varying frequency or wavelength selection, which could enable advanced applications like passive ranging and high-capacity communication.

Contribution

It introduces a novel approach linking phase spectrum slope to source distance through drifting frequency selection, enabling new distance measurement techniques.

Findings

Spectral shifts are proportional to source distances due to drifting frequency selection.

Phase spectrum slope serves as an asymptotic measure of source distance.

Potential applications include passive ranging and high-capacity communication systems.

Abstract

Any frequency selective device with an ongoing drift will cause observed spectra to be variously and simultaneously scaled in proportion to their source distances. The reason is that detectors after the drifting selection will integrate instantaneous electric or magnetic field values from successive sinusoids, and these sinusoids would differ in both frequency and phase. Phase differences between frequencies are ordinarily irrelevant, and recalibration procedures at most correct for frequency differences. With drifting selection, however, each integrated field value comes from *the sinusoid of the instantaneously selected frequency at its instantaneous received phase*, hence the waveform constructed by the integration will follow the drifting selection with a phase acceleration given by the drift rate times the slope of the received phase spectrum. A phase acceleration is literally a frequency shift, and the phase spectrum slope of a received waveform is an asymptotic measure of the source distance, as the path delay presents phase offsets proportional to frequency times the distance, and eventually exceeding all initial phase differences. Tunable optics may soon be fast enough for realizing such shifts by Fourier switching, and could lead to pocket X-ray devices; sources continuously variable from RF to gamma rays; capacity multiplication with jamming and noise immunity in both fibre and radio channels, passive ranging from ground to deep space; etc.