Error-Rate Characteristics of Oversampled Analog-to-Digital Conversion

1961 APPENDIX 1) m-sequences: We use the notation fa a ag to denote the sequence fa 1 ; a 2 ; 111g, and fa a a k g to denote the shifted sequence fa k+1 ; a k+2 ; 1 11g. We consider a binary m-sequence fa a ag with period P. Some properties of m-sequences which will be used in our discussion in Section IV are [10] • A1: One period of an m-sequence contains exactly (P + 1)=2 ones and (P 0 1)=2 zeros. • A2: Shift and add: For any k (k 6 = 0mod P), the sum of the m-sequence fa a ag and its k shift fa a a k g is another shift of the same m-sequence; i.e., (an 8 a n+k) = a n+l 8n where 8 denotes modulo two addition, and l is some other shift of the same sequence.