The relationship between the discrete Fourier transform (DFT) and the symmetrical/asymmetrical number system (SNS/ANS) is introduced in this paper. And the influence of noise upon the solution to the ambiguity problem in number system is also discussed. The principle of noise insensitive solution to the ambiguity in ANS system is extended to SNS system. The unambiguous bandwidth equations with noise protection in SNS are presented, based on which a real time noise insensitive algorithm in SNS for resolving undersampling ambiguous frequency is proposed.
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