Recursive Numerically-Controlled Polynomial Phase Signal Oscillator

This article is devoted to the development of a sample generator for polynomial phase signals. Known developments are limited to polynomial phase signals of the first (harmonic signals) and the second (linear frequency modulated signals). To construct them, tabular methods are used, which limit the possibilities of signal restructuring. This work is based on the use of a recursive approach, which minimizes the need for memory as much as possible and, thereby, increases the speed of parameter tuning. The authors have previously applied this approach to the generation of samples of chirp signals. Here the method is extended to arbitrary order complex polynomial phase signals. The proposed approach implies for the formation of a polynomial phase signal of the nth order a series connection of n identical units, the input parameters of which are the initial conditions. The units form complex samples of polynomial phase signals, the order of which is equal to the unit number. The input of the first unit is a zero-order polynomial phase signal - a complex constant. The initial conditions for the implementation of the former are the real coefficients of the nth degree polynomial and the signal amplitude. These parameters are used to calculate the initial conditions of the last block and the coefficients of the polynomials that determine the initial conditions of the previous blocks. Implementations of this approach for polynomial phase signals of the first, second and third order are presented. The Simulink model of the third order signal former is presented.