现实生活中的信号大多为连续信号

1、,Southeast University Department of Electrical Engineering,ADC and DAC,现实生活中的信号大多为连续信号，而计算机只能处理数字信号。模数转换（Analog-to-Digital Conversion ADC）和数模转换（Digital-to-Analog Conversion DAC）技术使得计算机可以处理现实生活中的信号了。数字信息有两个重要特征：它经过采样（sampled）得到的和它是经过量化（quantized）的，这两个因素限制了数字信号中包含信息的多少。,3.1 Quantization sample-and-hol

2、d (S/H) analog-to-digital converter (ADC),Southeast University Department of Electrical Engineering,ADC and DAC,Southeast University Department of Electrical Engineering,ADC and DAC,Southeast University Department of Electrical Engineering,ADC and DAC,采样就是把自变量（在这个例子里面是时间）由连续的变为离散的。 量化就是把应变量（这个例子里就是电

3、压）由连续的变为离散的。 数字化后的每一个采样点可能有的最大误差是 LSB（Least Significant Bit 最低有效位） 量化误差一个重要特性是它很像随机噪声，在大多数情况下它对信号带来的影响和随机噪声没有什么区别 量化误差是一种随机误差，所以AD的位数决定了数据的精度，于是我们可以这样说，如果把8位的AD换成12位的，将会提高测量的精度 。 考虑系统要采用多少位AD的时应注意的问题。 抖动（dithering） 什么时候不能把量化误差看作是随机噪声呢？ 用来提高对这样变化缓慢信号进行数字化精度的常用技术,Southeast University Department of Ele

4、ctrical Engineering,ADC and DAC,Southeast University Department of Electrical Engineering,ADC and DAC,3.2 Sampling Theorem 只要能从采样点重构出原来的连续信号就可以说前面的采样是正确的。,Southeast University Department of Electrical Engineering,ADC and DAC,采样定理是DSP技术的一个里程碑，也称为香农采样定理（Shannon sampling theorem），或奈奎斯特采样定理（Nyquist samp

5、ling theorem）。采样定理证明了采样频率必须为信号频率的两倍以上，采样数据才可以正确的重构出原始的模拟信号。 奈奎斯特频率（Nyquist frequency） 采样频率的一半 模拟信号中高于奈奎斯特频率以上的信息是无法包含在数字信号中。但是这些频率信息会混淆到数字信号所能表示的信息中。 任何高于奈奎斯特频率的频率都会对应到0到奈奎斯特频率之间,Southeast University Department of Electrical Engineering,ADC and DAC,Southeast University Department of Electrical Engin

6、eering,ADC and DAC,脉冲序列（impulse train） 一个连续信号，由一系列窄脉冲组成,Southeast University Department of Electrical Engineering,ADC and DAC,Southeast University Department of Electrical Engineering,ADC and DAC,3.3 Digital-to-Analog Conversion,Southeast University Department of Electrical Engineering,ADC and DAC,S

7、outheast University Department of Electrical Engineering,ADC and DAC,3.4 Analog Filters,antialias filter reconstruction filter,Southeast University Department of Electrical Engineering,ADC and DAC,Chebyshev Filter Butterworth Filter Bessel Filter 每一种滤波器的复杂程度可以级数（poles）和零点数（zeros）来调节 这三个名字表示的滤波器的类型，并

8、不是什么电阻、电容的特殊排列,Southeast University Department of Electrical Engineering,ADC and DAC,Sallen-Key circuit,Southeast University Department of Electrical Engineering,ADC and DAC,通过级联2，3，4个这样的电路形成4，6，8极的滤波器 每一个stage都有不同的k1和k2的参数，按照表3-1来选择。 高通滤波器就是把电路中R和C的位置互换一下,Southeast University Department of Electric

9、al Engineering,ADC and DAC,Switched capacitor filter,Southeast University Department of Electrical Engineering,ADC and DAC,stopband，passband,Southeast University Department of Electrical Engineering,ADC and DAC,Chebyshev最好，Bessel最差。可能正如你所想的，Chebyshev滤波器就是设计成这样的性质，具有很快的下降（roll-off）速度,Southeast Univer

10、sity Department of Electrical Engineering,ADC and DAC,Southeast University Department of Electrical Engineering,ADC and DAC,Chebyshev滤波器的passband上出现很多波动（ripple）。实际上Chebyshev之所以有较好的roll-off性质，就是这些passband ripple的存在 Butterworth可以提高较快的roll-off，而且passband中没有ripple Bessel的passband中也没有ripple，但roll-off比Butterworth要差很多,Southeast University Department of Electrical Engineering,ADC and DAC,step response,Southeast University Department of Electrical Engineering,ADC and DAC,Selecting The Antialias Filter,Southeast University De