Abstract:
A system capable of generating every possible data frame subperiod and delayed subperiod of a data frame of length of M clock pulse intervals (CPIs) comprises parallel modulo-mi counters. Each mi is a prime power divisor of M. Each mi pi Alpha i is a cascade of Alpha i identical modulo-pi counters, where mi p pi . The modulo-pi counters are feedback shift registers which cycle through pi distinct states. By this organization, every possible nontrivial data frame subperiod (in terms of clock pulse intervals) and delayed subperiod may be derived. Also, a specific CPI in the data frame may be detected. The number of clock pulses required to bring every (or a subset of all) modulopi counter to a respective designated state or count is determined by The Chinese Remainder Theorem. This corresponds to the solution of simultaneous congruences over relatively prime moduli.
Abstract:
Four classes of nonlinear nonsingular feedback shift registers (NLFSR) are disclosed. Each NLFSR, assumed to be r stages long, regardless of its class, generates a feedback sequence of length 2r. The sequence is one which cannot be completely deciphered by one not knowing the feedback arrangement, unless at least a very significant portion of the sequence, which is much greater than 2r-1 successive bits is known. Each NLFSR of either class 1 or class 2 has a feedback arrangement which is a function of a primative polynomial of degree r-1. Each register of class 1 includes three nonlinear terms, each one of which is the AND function of a different combination of (r-1) outputs of the first (r-1) stages. Each register of class 2 includes a single nonlinear term which is the AND function of (r-1) outputs of the first (r-1) stages. Each NLFSR in class 3 has a feedback arrangement which is based on a primative polynomial of degree r2 and a unique single nonlinear term, while each NLFSR in class 4 has a feedback arrangement which is based on a primitive polynomial of degree r-3 and three nonlinear terms.
Abstract:
A PN linear recurring binary sequence generator is described. It comprises a linear feedback shift register of r stages with three-tap feedback logic. The three stages which are fed back are i, j and r, wherein i
Abstract:
A feedback shift register (FSR) comprising a shift register of n stages, with the outputs of selected stages being mod-2 added in a feedback unit. The complement of the unit is fed back to the register''s input stage. The number of outputs, which are fed back, is always odd, equaling a number which is one less than 2, raised to a number representing the number of 1''s in the binary representation of n. The actual stages which are fed back are defined by the exponents of the terms X in the expansion of the term (X+1)n. Such an FSR produces disjointed multistate cycles, each of a length 2i, where
Abstract:
A digital function generator capable of generating any arbitrary single valued function representable by an independent and a dependent variable is disclosed. A state signal generator produces a plurality of output state signals corresponding to quantized sequential values of the independent variable. Predetermined ones of the quantized sequential signals correspond to predetermined incremental values of the dependent variable. A decoder monitors the output of the state signal generator and provides an output signal corresponding to the time of occurrence of the predetermined quantized sequential signals and the ''''sense'''' of the dependent variable change. A monitor provides an output signal which varies as a function of the decoder output. A digital-to-analog converter converts the monitor output to an analog signal representative of the function.