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Frequency estimation of multiple sinusoids is significant in both theory andapplication. In some application scenarios, only sub-Nyquist samples areavailable to estimate the frequencies. A conventional approach is to sample thesignals at several lower rates. In this paper, we address frequency estimationof the signals in the time domain through undersampled data. We analyze theimpact of undersampling and demonstrate that three sub-Nyquist channels aregenerally enough to estimate the frequencies provided the undersampling ratiosare pairwise coprime. We deduce the condition that leads to the failure ofresolving frequency ambiguity when two coprime undersampling channels areutilized. When three-channel sub-Nyquist samples are used jointly, thefrequencies can be determined uniquely and the correct frequencies areestimated. Numerical experiments verify the correctness of our analysis andconclusion.

Frequency Estimation of Multiple Sinusoids with Three Sub-Nyquist Channels