A phase match based frequency estimation method for sinusoidal signals

Abstract

Accurate frequency estimation affects the ranging precision of linear frequency modulated continuous wave (LFMCW) radars significantly. To improve the ranging precision of LFMCW radars, a phase match based frequency estimation method is proposed. To obtain frequency estimation, linear prediction property, autocorrelation, and cross correlation of sinusoidal signals are utilized. The analysis of computational complex shows that the computational load of the proposed method is smaller than those of two-stage autocorrelation (TSA) and maximum likelihood. Simulations and field experiments are performed to validate the proposed method, and the results demonstrate the proposed method has better performance in terms of frequency estimation precision than methods of Pisarenko harmonic decomposition, modified covariance, and TSA, which contribute to improving the precision of LFMCW radars effectively.

Phase difference estimation method based on data extension and Hilbert transform

“…(1) The coarse estimation ω 1 of signal frequency is gained by using the phase match-based frequency estimation method [15]. (2) Data extension signals x e and y e are calculated by utilizing equations ( 7)-( 9).…”

A spectrum matching method for accurate frequency estimation of real sinusoids

“…From [9,10], we know that if the signal is incoherently sampled, the signal autocorrelation has an error term which is only negligible for sufficiently large N. In frequency domain, the spectrum of the incoherently sampled signal suffers from interference from the negative frequency components, and it gets worse for small value of N. In addition, although the number of samples is increasing, the chosen value of 0  can hardly matches a frequency bin of the DFT, and so, it is inevitable to deal with the effect of incoherent sampling for accurate frequency estimation. Now, with a priori knowledge of the signal frequency, which is provided by the coarse estimation, the signal frequency can be directly modulated to approach coherent sampling.…”

“…However, coping with incoherently sampled data in short length, the EA method performs biased significantly because the signal autocorrelation has an error term which is not negligible. Accordingly, the recently proposed phase match based (PM) method [9] and phase correction autocorrelation (PCA) method [10] show different ways of reconstructing the autocorrelation function to avoid the error term, and besides, the Cauchy inequality is also considered to derive the error function in [9]. Generally, the PM and PCA methods are effective to deal with the incoherently sampled signal, but their performance still shows slight degradation when the signal lengths are very short.…”

A multifunction digital receiver suitable for real-time frequency detection and compensation in fast magnetic resonance imaging

“…In general, frequency detection of a single-tone sinusoidal signal in a narrow band is easily accomplished by using signal processing techniques. Many methods [14][15][16][17][18][19][20][21] have been reported, and the most representative being zero crossing detection, 14 peak detection, 15 Fourier Transformation (FT) methods, 15,16 and their variants. The majority of these methods are based on the periodic property of the signal.…”