Extraction of Pairs of Harmonics from Trigonometric Polynomials by Phase-Amplitude Operators

We propose a method for extracting the sums of two harmonics from trigonometric polynomials T n ( t ) by the method of amplitude-phase transformations. Such transformations send polynomials T n ( t ) to similar polynomials by two simplest operations: multiplication by a real constant X and shift by a real phase λ, i.e., T n ( t ) → X ・ T n ( t − λ). The harmonics are extracted by adding similar polynomials.