A Generalized Chinese Remainder Theorem for Two Integers

A generalized Chinese remainder theorem (CRT) for the determination of two integers is studied in this letter, where the correspondence between the remainders and the two integers in each residue set is not known. A better range than the existing known ones of two integers that can be uniquely determined from their residue sets is first obtained. Then, a closed-form and simple determination algorithm is proposed. Finally, a better sufficient condition on the range of determinable two integers is obtained when the number of erroneous residue sets is given. The study is motivated and has applications in the determination of multiple frequencies from multiple undersampled waveforms.