Abstract
This paper proposes a novel phase estimator based on fully-traversed Discrete Fourier Transform (DFT) which takes all possible truncated DFT spectra into account such that it possesses two merits of ‘direct phase extraction’ (namely accurate instantaneous phase information can be extracted without any correction) and suppressing spectral leakage. This paper also proves that the proposed phase estimator complies with the 2-parameter joint estimation model rather than the conventional 3-parameter joint model. Numerical results verify the above two merits and demonstrate that the proposed estimator can extract phase information from noisy multi-tone signals. Finally, real data analysis shows that fully-traversed DFT can achieve a better classification on the phase of steady-state visual evoked potential (SSVEP) brain-computer interface (BCI) than the conventional DFT estimator does. Besides, the proposed phase estimator imposes no restrictions on the relationship between the sampling rates and the stimulus frequencies, thus it is capable of wider applications in phase-coded SSVEP BCIs, when compared with the existing estimators.
Highlights
Estimating the frequency, the phase and the amplitude of a signal is a standard classical problem of signal processing
Phase estimators based on direct Discrete Fourier Transform (DFT) are the mainstream [5]
To further verify the superiority of the proposed phase estimator, simulations performed under various noisy conditions and different spectral orders are presented
Summary
Estimating the frequency, the phase and the amplitude of a signal is a standard classical problem of signal processing. Phase estimators based on direct Discrete Fourier Transform (DFT) are the mainstream [5]. In [5], Liguori pointed out that, the existing DFT-based phase estimators heavily rely on the result of frequency estimate. To illustrate this dependency, let us study the sampled version (the sampling rate is Fs ) of a complex exponential signal x (t) = a0 exp[ j(2π f 0 t + θ0 )] as x (n) = x (t) t=n∆t. Where a0 , f 0 , θ0 are amplitude, frequency and phase respectively and ∆t is the sampling interval 1/Fs. the frequency resolution of the N-point DFT X (k) is ∆ f = Fs /N = 1/N∆t.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
