Quadrature complement method for time-resolved signal frequency reconstruction

The Doppler-signal processing method based on two integral convolutions with respect to approximate Doppler phase, φ(t), being a variable is introduced. While reducing the noise, these transforms produce the first Doppler harmonic, S₁ ^‖(t), and its quadrature complement, S₁ ^⊥(t). The complex harmonic, s₁(t)=S₁ ^‖(t)+iS₁ ^⊥(t), makes it possible to find a new approximation of both Doppler signal frequency ω_D(t) and phase φ(t), as well as the rms frequency error, χ_ω (t), used to regularize the solution. The iterative procedure to estimate frequency ω_D(t), which converges in the mean to χ_ω (t)-vicinity of Doppler frequency, Ω_D(t), is proposed. Kernels of transforms are defined on the phase interval [-πn; +πn] for n ≥ 2. Method resolution is R_rs = n/2 beats periods, and for n = 2, it equals the Doppler period, while the error is χ_ω (t)∼n^-3/2. Example velocity profiles are reconstructed from two experimental Doppler signals.