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Study of digital recursive generators of samples of complex harmonic signals
Authors
	Naumovich T.V.
Date of publication
	2021
DOI
	10.31114/2078-7707-2021-4-106-113
Abstract
	The article describes the results of a study of digital recursive oscillators of a complex harmonic signal samples. The considered oscillators were interpreted as unstable recursive complex digital filters, the poles of which are located on the contour of the unit circle in the z-plane. The oscillators, which were studied in our previous publications, were special cases of recursive generators of samples of polynomial-phase signals. Harmonic signals are polynomial-phase signals of the first degree. These oscillators are characterized by the fact that quantization in the structure of these oscillators leads to the fact that the poles of the corresponding digital filters can be located in the z-plane only at the nodes of a square lattice with a step determined by the bit depth. For this reason, the poles cannot be located on the contour of the unit circle in the z-plane. They either move inside the unit circle, causing the generated oscillations to damp, or go beyond the unit circle, as a result of which the filter output signal is fell apart. Taking into account the earlier studies in the field of synthesis of recursive digital filters with a finite word length, the analysis of structures in which quantization leads to the fact that the allowed positions of the poles are the intersection points of a system of concentric circles with a system of parallel equidistant straight lines parallel to the ordinate axis are carried out. In these structures, it is possible to "fix" the poles on the unit circle. As a result, it is possible to form counts of continuous oscillations. The simulation of the process of forming signal samples in Simulink is described.
Keywords
	Direct digital synthesis, polynomial phase signals, recursive signal generation, quantization, structures of oscillators.
Library reference
	Naumovich T.V. Study of digital recursive generators of samples of complex harmonic signals // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2021. Issue 4. P. 106-113. doi:10.31114/2078-7707-2021-4-106-113
URL of paper
	http://www.mes-conference.ru/data/year2021/pdf/D080.pdf