A New Approach for the DFT NIST Test Applicable for Non-Stationary Input Sequences

Abstract

The National Institute of Standards and Technology (NIST) document is a list of fifteen tests for estimating the probability of signal randomness degree. Test number six in the NIST document is the Discrete Fourier Transform (DFT) test suitable for stationary incoming sequences. But, for cases where the input sequence is not stationary, the DFT test provides inaccurate results. For these cases, test number seven and eight (the Non-overlapping Template Matching Test and the Overlapping Template Matching Test) of the NIST document were designed to classify those non-stationary sequences. But, even with test number seven and eight of the NIST document, the results are not always accurate. Thus, the NIST test does not give a proper answer for the non-stationary input sequence case. In this paper, we offer a new algorithm or test, which may replace the NIST tests number six, seven and eight. The proposed test is applicable also for non-stationary sequences and supplies more accurate results than the existing tests (NIST tests number six, seven and eight), for non-stationary sequences. The new proposed test is based on the Wigner function and on the Generalized Gaussian Distribution (GGD). In addition, this new proposed algorithm alarms and indicates on suspicious places of cyclic sections in the tested sequence. Thus, it gives us the option to repair or to remove the suspicious places of cyclic sections (this part is beyond the scope of this paper), so that after that, the repaired or the shortened sequence (original sequence with removed sections) will result as a sequence with high probability of random degree.