a~n序列伪随机多频信号数学分析及实现

利用-1,0,1这3个元素的3元数加法群自封闭加法的编码原理,建立将多种频率信号合成、编码的a~n序列伪随机多频信号.以2~n系列伪随机多频信号的时域表达式为基础,构建可用数字逻辑实现的二进制序列,利用复杂可编程逻辑器件(CPLD)及其软件实现伪随机多频信号的发射波形.研究结果表明:其波形既具有某种随机波形的特征,又能事先设定,可重复产生;其序列主频率信号强度基本相等并不随频率增大而减弱,频点在对数坐标系上等间距,分布合理.

Mathematical analysis and realization of a~n sequence pseudo-random multi-frequencies signal

a~n sequence pseudo-random multi-frequencies signal is the sequence of synthesis and code of multi-kind frequencies signal using the code principle of self-given addition, i.e., the addition group of three elements that are -1,0 and 1. Based on time domain expression of 2~n sequence pseudo-random multi-frequency signal, the binary system sequence realized by numeral logic was formed, and complex programmable logic device (CPLD) and its soft were used to realize pseudo-random multi-frequencies signal's transmitting wave. Signal's transmitting wave not only takes on the characteristic of certain random wave, but also can be set in advance and created repeatedly. Its signal amplitudes of the main frequencies are basically equal, the amplitudes won't be weakened when the frequency increases, and the interval between the adjoining main frequencies is even and reasonable in logarithmical coordinate.