Quadrature complement method for time-resolved signal frequency reconstruction

Area of Science:

• Signal Processing
• Applied Physics
• Biomedical Engineering

Background:

• Doppler signal processing is crucial for various applications, including medical imaging and fluid dynamics.
• Existing methods often struggle with noise reduction and accurate frequency estimation.
• The need for robust algorithms to extract precise Doppler parameters is evident.

Purpose of the Study:

• To introduce a new Doppler-signal processing method based on integral convolutions.
• To enhance noise reduction capabilities while accurately estimating Doppler signal frequency and phase.
• To develop an iterative procedure for improved Doppler frequency estimation and regularization.

Main Methods:

• The method utilizes two integral convolutions with respect to the approximate Doppler phase, φ(t).
• It generates the first Doppler harmonic, S₁^‖(t), and its quadrature complement, S₁^⊥(t).
• An iterative procedure is proposed for estimating Doppler frequency ω_D(t) with defined transform kernels and resolution.

Main Results:

• The transforms effectively reduce noise and produce the complex harmonic s₁(t) = S₁^‖(t) + iS₁^⊥(t).
• This enables accurate approximation of Doppler signal frequency, phase, and root-mean-square frequency error.
• The iterative method converges to the Doppler frequency within the χ_ω(t)-vicinity, with error scaling as χ_ω(t)∼n^-3/2.

Conclusions:

• The proposed Doppler-signal processing method offers improved noise reduction and parameter estimation.
• It provides a new approximation for Doppler frequency and phase, crucial for accurate signal analysis.
• The method's effectiveness is demonstrated through the reconstruction of velocity profiles from experimental Doppler signals.