离散时间信号处理PPT连续时间信号的采样.pptVIP

4 SAMPLING OF CONTINUOUS-TIME SIGNALS 4.0 INTRODUCTION Discrete-time signals can arise in many ways ,but they most commonly occur as representations of sampled continuous-time signals. It is remarkable that under reasonable constraints, a continuous-time signal can be quite accurately represented by samples taken at discrete points in time. 4.1 PERIODIC SAMPLING The typical method of obtaining a discrete-time representation of a continuous-time signals is through periodic sampling, wherein a sequence of samples, is obtained from a continuous-time signal according to the relation T is the sampling period, and its reciprocal, is the sampling frequency in samples per second. We also express the sampling frequency as when we want to use frequency in radians per second. In a practical setting , the operation of sampling is implemented by an analog-to-digital (A/D) converter. Such system can be viewed as approximations to the ideal C/D converter. It is convenient to represent the sampling process mathematically in the two stages depicted in Figure 4.2 (a). The stages consist of an impulse train modulator followed by conversion of the impulse train to a sequence. Figure4.2(b) shows a continuous-time signal and the results of impulse train sampling for two different sampling rates. 讨论： 1）A0=a0 ——常量，与频率无关（直流分量、零频分量） 2）Ancos(n?t+?0 )——正弦量，与n有关（谐波分量） 3）谐波分类： 讨论： 4）函数对称性与谐波的成份 例： 图示电压中，T=2?，求u(t)傅立叶级数展开式。 4.2 FREQUENCY-DOMAIN REPRESENTATION OF SAMPLING To derive the frequency-domain relation between the input and output of an ideal C/D converter, let us first consider the conversion of to through modulation of the periodic impulse train Where is the unit impulse function, or Dirac delta function . We modulate with , obtaining Let us now consider the Fourier transform of . and is the product of