摘要
从Fourier级数出发 ,到任意闭区间上可积函数的Fourier分析 ,给出了数字信号Fourier分析的理论基础。以字符“b”为例 ,建立了严格的数学模型 ,严密推导了Fourier系数表达式。阐明了Fourier级数的“项”和“n阶Fourier级数”(前n项和 )的概念。详尽地分析了信道通频带B与Fourier阶数n(展开式“保留”项 )的关系。借助计算机计算了n≤ 10 0时各Fourier级数项和前n项和 ,并用Plot将计算结果绘成曲线 ,获得n≤10 0时各级Fourier展开曲线。与数字信号对照 ,Fourier级数的取项与波形的关系显而易见 ,特别是n取值较小时 ,Fourier级数取项少 ,波形失真严重 ;所以在B一定时传输速率不能过高 ,否则 ,由于波形失真而导致信号出错。
Based on Fourier progression, the theoretical basis of Fourier analysis for digital signal was given by the Fourier analysis of any function which was defined in a close interzone and could be integrated correctly. The mathematical theory for Fourier analysis of digital signals was given. The critical mathematical model of 'b', for instance was set up. Based on the model, the Fourier coefficients of 'b' were accurately calculated. The conceptions of Fourier term and Fourier progression containing n terms were clarified. The relation between the transmission bands B of a channel and the value of n in Fourier progression was analyzed in detail. Assisted with computer, we accurately calculated each Fourier term and an n rank Fourier progression as n wasn't more than 100. The results were input into Plot software and transformed into plots. Compared with digital signal model, the models of Fourier plots depended strongly on the value of n. The smaller the value of n, the less the terms of the Fourier procession, and the more severely the model of Fourier plot deviated. As a result, to a certain B, the transmitting rate can't get too high, or mistake would occur because of wave distortion.
出处
《光谱学与光谱分析》
SCIE
EI
CAS
CSCD
北大核心
2003年第4期820-822,共3页
Spectroscopy and Spectral Analysis
