Non-parametric estimation of the amplitude ratio of sinusoidal signals with common frequency

The systematic bias error of the amplitude ratio estimation owed to leakage effect can be effectively reduced by employment of the non-parametric multi-point interpolation of the discrete Fourier transform in the quotient of amplitudes. Simple single-step algorithms for fast measurement and estimation of the amplitude ratio of sinusoidal signals with the same frequency from two channels are presented. The paper analyzes and compares the systematic bias errors and the noise error behaviors of the amplitude ratio estimation changing the order of Rife-Vincent windows class I, which are designed for maximization of the window spectrum side-lobe fall-off, and minimum side-lobe level (MSL) windows, which are designed for minimization of the energy in the window spectrum main lobe. Estimation errors are shown in relation to the number of signal cycles in the measurement interval.