  Extraction of harmonics of a given order from real trigonometric polynomials
(signals) is one of the main problems in harmonic analysis. It has many
applications in physics, radio and electrical engineering, in particular, in
filtration of harmonic signals of different nature. There exist many methods
(mainly, approximative) for solution of this problem. The most common ones are
spectral methods based on Fourier transform and other resonance principles.
  In this paper we propose a new method for extracting harmonics by amplitude
and phase transformation of trigonometric polynomials. These transformations
use the two simplest operations -- multiplication by a real constant and phase
shift -- to obtain polynomials similar to the initial ones. A harmonic is
extracted by an amplitude and phase operator that simply overlays (sums up) a
finite number of such similar polynomials. The overlay method enables us to
obtain precise analytical formulas for calculating harmonics of a given order.
