A new algorithm is suggested based on the central limit theorem for generating pseudo-random numbers with a specified normal or Gaussian probability density function. The suggested algorithm is very simple but highly ...A new algorithm is suggested based on the central limit theorem for generating pseudo-random numbers with a specified normal or Gaussian probability density function. The suggested algorithm is very simple but highly accurate, with an efficiency that falls between those of the Box-Muller and von Neumann rejection methods.展开更多
The National Institute of Standards and Technology (NIST) document is a list of fifteen tests for estimating the probability of signal randomness degree. <span style="font-family:Verdana;">Test number ...The National Institute of Standards and Technology (NIST) document is a list of fifteen tests for estimating the probability of signal randomness degree. <span style="font-family:Verdana;">Test number six in the NIST document is the Discrete Fourier Transform</span><span style="font-family:Verdana;"> (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 </span><span style="font-family:Verdana;">or test, which may replace the NIST tests number six, seven and eight. The</span> <span style="font-family:Verdana;">proposed test is applicable also for non-stationary sequences and supplies</span><span style="font-family:Verdana;"> more </span><span style="font-family:Verdana;">accurate results than the existing tests (NIST tests number six, seven and</span><span style="font-family:Verdana;"> eight), for non-stationary sequences. The new proposed test is based on the Wigner function and on the Generalized Gaussian Distribution (GGD). In addition, </span><span style="font-family:Verdana;">this new proposed algorithm alarms and indicates on suspicious places of</span><span style="font-family:Verdana;"> cyclic </span><span style="font-family:Verdana;">sections in the tested sequence. Thus, it gives us the option to repair or to</span><span style="font-family:Verdana;"> remove the suspicious places of cyclic sections</span><span><span><span><span></span><span></span><b><span style="font-family:;" "=""><span></span><span></span> </span></b></span></span></span><span><span><span><span></span><span></span><span style="font-family:;" "=""><span></span><span></span><span style="font-family:Verdana;">(this part is beyond the scope </span><span style="font-family:Verdana;">of this paper), so that after that, the repaired or the shortened sequence</span><span style="font-family:Verdana;"> (origi</span><span style="font-family:Verdana;">nal sequence with removed sections) will result as a sequence with high</span><span style="font-family:Verdana;"> probability of random degree.</span></span></span></span></span>展开更多
文摘A new algorithm is suggested based on the central limit theorem for generating pseudo-random numbers with a specified normal or Gaussian probability density function. The suggested algorithm is very simple but highly accurate, with an efficiency that falls between those of the Box-Muller and von Neumann rejection methods.
文摘The National Institute of Standards and Technology (NIST) document is a list of fifteen tests for estimating the probability of signal randomness degree. <span style="font-family:Verdana;">Test number six in the NIST document is the Discrete Fourier Transform</span><span style="font-family:Verdana;"> (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 </span><span style="font-family:Verdana;">or test, which may replace the NIST tests number six, seven and eight. The</span> <span style="font-family:Verdana;">proposed test is applicable also for non-stationary sequences and supplies</span><span style="font-family:Verdana;"> more </span><span style="font-family:Verdana;">accurate results than the existing tests (NIST tests number six, seven and</span><span style="font-family:Verdana;"> eight), for non-stationary sequences. The new proposed test is based on the Wigner function and on the Generalized Gaussian Distribution (GGD). In addition, </span><span style="font-family:Verdana;">this new proposed algorithm alarms and indicates on suspicious places of</span><span style="font-family:Verdana;"> cyclic </span><span style="font-family:Verdana;">sections in the tested sequence. Thus, it gives us the option to repair or to</span><span style="font-family:Verdana;"> remove the suspicious places of cyclic sections</span><span><span><span><span></span><span></span><b><span style="font-family:;" "=""><span></span><span></span> </span></b></span></span></span><span><span><span><span></span><span></span><span style="font-family:;" "=""><span></span><span></span><span style="font-family:Verdana;">(this part is beyond the scope </span><span style="font-family:Verdana;">of this paper), so that after that, the repaired or the shortened sequence</span><span style="font-family:Verdana;"> (origi</span><span style="font-family:Verdana;">nal sequence with removed sections) will result as a sequence with high</span><span style="font-family:Verdana;"> probability of random degree.</span></span></span></span></span>
