“Natural” and “Technical” Shapes of the Bispectral Peak of a Triharmonic Oscillation

Abstract

By analogy with the spectral-line profile characterizing the stability of a single quasi-harmonic oscillation, we study physical limits of stability and phase synchronism of a triharmonic oscillation (triplet) characterized by the shape of its bispectral “peak.” The triplet is the standard (test) signal for new-generation radiophysical devices, i.e., bispectral analyzers as well as the elementary component of highly informative bispectral signals. The problem of “natural” and “technical” shapes of the bispectral peak is analyzed. Bispectral analogs of the natural and technical broadening of spectral lines of self-oscillations with physically determined fluctuations of the component frequencies are proposed. It is shown that these characteristics can be observed and measured simultaneously. Universal shapes of three-dimensional bispectral peaks for extremely slow and extremely fast fluctuations, exponentially correlated fluctuations, and 1/f frequency fluctuations are found. The phenomenon of bispectral-peak superlocalization is analyzed. The obtained peak shapes and their effective cross-sectional areas characterize the ultimate attainable resolution of bispectral analyzers and information capacity of the synthesized bispectral structures.