Quasi-Uniform Sequence Analytical Description of the First Type Pulses

At present, passive digital frequency synthesis systems are increasingly used in exciters of radio transmitting devices and in heterodynes of radio receiving devices of radar, radio navigation and radio communication systems. Such systems are based on a finite state machine - a device or program that can change its states at discrete moments of time, integer multiples of the clock interval, have a finite number of stable states, i.e. have a finite memory. Therefore, the problem of analytical description of the states of such machines at any predetermined moment of time is relevant.The purpose of this work is to compactly describe the transition functions and output functions of machines used in passive digital frequency synthesis systems. An essential feature of the analysis and design of such machines is the requirement to minimize the level of functional phase-pulse modulation of the output pulse flow, i.e. minimization of the time error between the flow of generated pulses and the ideally uniform (hypothetical) flow of pulses of the required frequency. A quasi-periodic pulse sequence with a minimum time deviation from the hypothetical sequence is called a quasi-uniform pulse sequence. In addition, the purpose of this work is to correctly prove the optimality of a quasi-uniform sequence from the point of view of the minimum functional phase-pulse modulation of the output pulse flow.The research methods are based on the use of number-theoretical transformations of the main parameter of the machine - its division coefficient N = P / Q, where P and Q, respectively, are the number of clock and output pulses in the period of non-uniformity of the output flow of the quasi-uniform sequence.Result. New analytical expressions for describing the states of the machine at any predetermined moment of time, expressions for the instantaneous (current) phase of the machine and the instantaneous (current) frequency of the quasi-uniform pulse sequence at its output are obtained. Such expressions are convenient for analyzing and calculating machines used in passive digital frequency synthesis systems.The theoretical significance lies in the development of a method for describing the states of an optimal finite state machine in the time domain and obtaining the corresponding analytical expressions.

frequency synthesis, finite state machine, transition function, output function, continued fraction, rational number, quasi-uniform pulse sequence, functional phase-pulse modulation