A new robust Chinese remainder theorem with improved performance in frequency estimation from undersampled waveforms

• A new robust CRT is proposed when multiple unrestricted errors combined with an arbitrary number of small errors are in the remainders.
• A new robust reconstruction algorithm is proposed.
• The proposed algorithm leads to a better performance in frequency estimation from undersampled waveforms than the previous one.

A robust Chinese remainder theorem (CRT) has been recently proposed, that is, a large integer less than the least common multiple (lcm) of all the moduli can be robustly reconstructed from its erroneous remainders when all remainder errors are assumed small. In this paper, we propose a new robust CRT when a combined occurrence of multiple unrestricted errors and an arbitrary number of small errors is in the remainders, where a determinable integer is required to be less than the lcm of a subset of the moduli. A reconstruction algorithm is also proposed. We then apply the reconstruction algorithm to frequency estimation from undersampled waveforms. It shows that the newly proposed algorithm leads to a better performance than the previous existing robust CRT algorithm.