System employing continuous-time dissipative pseudorandom dynamics for

Abstract

A communication and/or measurement system includes in a a transmitter an analog feedback system that modulates a pseudo-random noise signal with a message signal to produce a wideband signal for transmission. A receiver, which demodulates the wideband signal to recover the message signal, includes an associated analog feedback system that reproduces the noise signal based on the received signal. The analog feedback systems (AFS) are continuous-time generalizations of a linear feedback shift register ('LFSR'). The AFS are characterized by a function that agrees with the function that characterizes the LFSR, at the points at which that function is defined. Further, the AFS characterizing function has stable periodic orbits at these values, and the stable periodic orbits are attractors. The AFS thus produces a signal that relaxes on to a nearest periodic orbit that generalizes to continuous time the maximal sequence produced by the corresponding LFSR. The AFS in the transmitter, which operates in accordance with a harmonic oscillator, is characterized by the following differential equation: ##EQU1## where the .alpha..sub.i 's are the coefficients of the maximum length polynomial used to produce the maximal sequence. The AFS in the receiver is characterized by the following differential equation: ##EQU2##