arXiv subjects

Haijian Zhang

Publications and source records attributed to Haijian Zhang.

24 records · Page 2Linked to original sources

arXiv2017

An algorithm of frequency estimation for multi-channel coprime sampling

In some applications of frequency estimation, it is challenging to sample at as high as the Nyquist rate due to hardware limitations. An effective solution is to use multiple sub-Nyquist channels with coprime undersampling ratios to jointly sample. In this paper, an algorithm suitable for any number of channels is proposed, which is based on subspace techniques. Numerical simulations show that the proposed algorithm has high accuracy and good robustness.

cs.IT↗

arXiv2017

Frequency Estimation of Multiple Sinusoids with Three Sub-Nyquist Channels

Frequency estimation of multiple sinusoids is significant in both theory and application. In some application scenarios, only sub-Nyquist samples are available to estimate the frequencies. A conventional approach is to sample the signals at several lower rates. In this paper, we address frequency estimation of the signals in the time domain through undersampled data. We analyze the impact of undersampling and demonstrate that three sub-Nyquist channels are generally enough to estimate the frequencies provided the undersampling ratios are pairwise coprime. We deduce the condition that leads to the failure of resolving frequency ambiguity when two coprime undersampling channels are utilized. When three-channel sub-Nyquist samples are used jointly, the frequencies can be determined uniquely and the correct frequencies are estimated. Numerical experiments verify the correctness of our analysis and conclusion.

cs.IT↗

arXiv2016

Line Spectral Estimation Based on Compressed Sensing with Deterministic Sub-Nyquist Sampling

As an alternative to the traditional sampling theory, compressed sensing allows acquiring much smaller amount of data, still estimating the spectra of frequency-sparse signals accurately. However, compressed sensing usually requires random sampling in data acquisition, which is difficult to implement in hardware. In this paper, we propose a deterministic and simple sampling scheme, that is, sampling at three sub-Nyquist rates which have coprime undersampled ratios. This sampling method turns out to be valid through numerical experiments. A complex-valued multitask algorithm based on variational Bayesian inference is proposed to estimate the spectra of frequency-sparse signals after sampling. Simulations show that this method is feasible and robust at quite low sampling rates.

cs.IT↗

arXiv2016

Frequency Estimation of Multiple Sinusoids with Sub-Nyquist Sampling Sequences

In some applications of frequency estimation, the frequencies of multiple sinusoids are required to be estimated from sub-Nyquist sampling sequences. In this paper, we propose a novel method based on subspace techniques to estimate the frequencies by using under-sampled samples. We analyze the impact of under-sampling and demonstrate that three sub-Nyquist sequences are general enough to estimate the frequencies under some condition. The frequencies estimated from one sequence are unfolded in frequency domain, and then the other two sequences are used to pick the correct frequencies from all possible frequencies. Simulations illustrate the validity of the theory. Numerical results show that this method is feasible and accurate at quite low sampling rates.

cs.IT↗

arXiv2015

A Class of Deterministic Sensing Matrices and Their Application in Harmonic Detection

In this paper, a class of deterministic sensing matrices are constructed by selecting rows from Fourier matrices. These matrices have better performance in sparse recovery than random partial Fourier matrices. The coherence and restricted isometry property of these matrices are given to evaluate their capacity as compressive sensing matrices. In general, compressed sensing requires random sampling in data acquisition, which is difficult to implement in hardware. By using these sensing matrices in harmonic detection, a deterministic sampling method is provided. The frequencies and amplitudes of the harmonic components are estimated from under-sampled data. The simulations show that this under-sampled method is feasible and valid in noisy environments.

cs.IT↗

arXiv2015

Joint Frequency Estimation with Two Sub-Nyquist Sampling Sequences

In many applications of frequency estimation, the frequencies of the signals are so high that the data sampled at Nyquist rate are hard to acquire due to hardware limitation. In this paper, we propose a novel method based on subspace techniques to estimate the frequencies by using two sub-Nyquist sample sequences, provided that the two under-sampled ratios are relatively prime integers. We analyze the impact of under-sampling and expand the estimated frequencies which suffer from aliasing. Through jointing the results estimated from these two sequences, the frequencies approximate to the frequency components really contained in the signals are screened. The method requires a small quantity of hardware and calculation. Numerical results show that this method is valid and accurate at quite low sampling rates.

cs.IT↗