Digital estimation of frequencies of sinusoids from wide-band under-sampled data

Tufts, D.W.; Ge, Hongya

doi:10.1109/icassp.1995.479554

Cited by 14 publications

(7 citation statements)

References 6 publications

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“…However, this solves the frequency ambiguity for a single tone only. The work in [2] proposes an approach that requires (N+1) co-prime timedelays and (N+1) ADCs for estimating N frequency components. But even in narrow band systems N is typically large, making this approach impractical.…”

Section: Introduction and Prior Artmentioning

confidence: 99%

Reconstructing Aliased Frequency Spectra by Using Multiple Sample Rates

Huiskamp

Alink

Nauta

et al. 2022

IEEE Trans. Circuits Syst. I

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A novel algorithm is presented that can resolve frequency ambiguity that arises from sampling a set of signals spanning more than a single Nyquist zone. The method uses two samplers, each sampling the same input signal with different (non-integer multiple) sampling rates. The algorithm is able to resolve frequency ambiguity and reconstruct signals with an orthogonal frequency basis spanning multiple Nyquist zones, provided that the aggregate information-bearing bandwidth of the signals is less than half the cumulative data converter sampling rates. This manuscript describes the theoretical background for the algorithm and validates it through measurements performed on a test-board comprising of two 10 bit analog-todigital converters clocked at two different (non-integer multiple) sample rates. Measurements show that even in the presence of aliasing, an orthogonal signal spanning multiple Nyquist zones can be fully reconstructed.

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Section: Introduction and Prior Artmentioning

confidence: 99%

Reconstructing Aliased Frequency Spectra by Using Multiple Sample Rates

Huiskamp

Alink

Nauta

et al. 2022

IEEE Trans. Circuits Syst. I

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show abstract

“…To avoid the frequency ambiguity, Zoltowski proposed a time delay method which requires the time delay difference of the two sampling channels less than or equal to the Nyquist sampling interval [11]. By introducing properly chosen delay lines, and by using sparse linear prediction, the method in [12] provided unambiguous frequency estimates using low A/D conversion rates. The authors of [13] made use of Chinese Remainder Theorem (CRT) to overcome the ambiguity problem, but only single frequency determination is considered.…”

Section: Introductionmentioning

confidence: 99%

Frequency estimation of multiple sinusoids with three sub-Nyquist channels

et al. 2017

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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.

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“…To avoid the frequency ambiguity, Zoltowski proposed a time delay method which requires the time delay difference of the two sampling channels less than or equal to the Nyquist sampling interval [8]. By introducing properly chosen delay lines, and by using sparse linear prediction, the method in [9] provided unambiguous frequency estimates using low A/D conversion rates. The authors of [10] made use of Chinese Remainder Theorem (CRT) to overcome the ambiguity problem, multiple signal frequencies often need the parameter pairing.…”

Section: Introductionmentioning

confidence: 99%

Joint Frequency Estimation with Two Sub-Nyquist Sampling Sequences

Huang¹,

Sun²,

Yu³

et al. 2015

Preprint

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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.

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Digital estimation of frequencies of sinusoids from wide-band under-sampled data

Cited by 14 publications

References 6 publications

Reconstructing Aliased Frequency Spectra by Using Multiple Sample Rates

Reconstructing Aliased Frequency Spectra by Using Multiple Sample Rates

Frequency estimation of multiple sinusoids with three sub-Nyquist channels

Joint Frequency Estimation with Two Sub-Nyquist Sampling Sequences

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