Generalized Rudin-Shapiro Sequences: Construction and Properties

• Main Authors: Huang, Tao-Hsien, 黃道賢
• Other Authors: 黃之浩
• Format: Others
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/9p4vdq

碩士 === 國立清華大學 === 通訊工程研究所 === 103 === In this thesis, we generalized the Rudin-Shapiro sequences from binary to q-ary case (where q>1). Different from the original binary Rudin-Shapiro sequences, our generalized sequences take values from the unit circle on the complex plane. Therefore, our generalized sequences are more practical than original ones. We simulated our proposed q-ary sequences using C and MATLAB and compared their properties with original binary ones. We focused our discussion on the following three aspects: recursive properties, existence of upper/lower bounds as well as their magnitudes. Regarding their recursive properties, we derived their general construction formula in the q-ary case. Second, we showed that the existence of bound and found that its order locates at √n by analyzing simulation data. Furthermore, we estimated their upper/lower bounds where 3≤q≤8, and observed and analyzed their corresponding values. We found a very unusual periodic property when vertical axis was divided by √n and the horizontal axis representing the sum of sequence elements was on log scale. Such settings lead to certain unusually similar patterns when the sequence length becomes longer. We observed this property and derived the general form of the location where local maximum/minimum happens.