电子信息工程专业毕业论文--方波信号波形合成电路的设计.doc

电子信息工程专业毕业论文--方波信号波形合成电路的设计
摘要
课题任务是对一个特定频率的方波进行变换产生多个不同频率的弦信号,再将这些正弦信号合成为近似方波。首先设计制作一个特定频率的方波发生器,并在这个方波上进行必要的信号转换,分别产生 10KHz、30KHz 和 50KHz 的正弦波,然后对这三个正弦波进行频率合成,合成后的目标信号为10KHz近似方波。
本课题的理论基础是傅里叶级数。法国数学家傅里叶发现,任何周期函数都可以用正弦函数和余弦函数构成的无穷级数来表示(选择正弦函数与余弦函数作为基函数是因为它们是正交的),后世称为傅里叶级数一种特殊的三角级数。[1]
随着傅里叶级数中计算的项的增加,级数会越来越近似于定义复杂信号波形的精确函数。计算机能够计算出傅里叶级数的成百上千甚至数百万个项。
本课题就是基于此原理,取基波、三次谐波及五次谐波进行合成。当然谐波之间要满足一定相位及幅值比例关系,所以用同一振荡器产生信号,再进行分频及移相等处理。
关键词: 方波振荡器; 傅里叶级数;分频; 滤波; 移相电路
Abstract
Mission is to issue a specific frequency square wave to transform strings produce multiple signals of different frequencies, then the synthesis of these sine square wave signal. First, to design a specific frequency square wave generator, and in this square wave signal on the need for conversion, were generated 10KHz, 30KHz and 50KHz sine wave, then a frequency of the three sine wave synthesis, synthesis of the target after 10KHz square wave signal.
The project is based on Fourier series theory. French mathematician Fourier discovered that any periodic function can be used sine and cosine functions to represent the infinite series form select the sine function and cosine function as basis functions because they are orthogonal , later known as the Fourier A special series of triangular series. Suppose a0, a1, a2, a3, ..., an, ... and b1, b2, b3, ..., bn, ... is a set of infinite constant. These constants are called Fourier coefficients. x is a variable. Ordinary Fourier series can be expressed as:
F x a0/2 + a1 cos x + b1 sin x + a2 cos 2x + b2 sin 2x + ...+ an cos nx + bn sin nx + ...
Some relatively simple waveforms, such as pure sine wave, but these are only theoretical. In real life, most of the waveforms contain harmonic frequency minimum frequency or a multiple of the fundamental frequency energy. Harmonic frequency pared to the ratio of the fundamental frequency energy is dependent on the waveform. Fourier series mathematical definition of this kind of waveform relative to the displacem