Phase regression approach for estimating the parameters of a noisy multifrequency signal

A novel approach for estimating the parameters of a multifrequency signal from discrete samples corrupted by additive noise is presented. An established mathematical model indicates that noise influence on the discrete phase and amplitude spectra is equivalent to additive phase and amplitude noise, respectively. On this basis, a simple algorithm is proposed to estimate the frequency and phase of each sinusoid component by linear regression on the phase spectra of segmented signal blocks, while an amplitude estimator is directly derived from the spectrum of the window function. The circular nature of the phase spectrum is thoroughly explored. Also, an algorithmic scheme is presented. The derived variances of the estimators show that for a noisy signal this approach provides superior accuracy over the traditional approaches. Simulations and engineering application confirm the validity of the presented method.