信號(hào)與系統(tǒng)英文版課件：Chap7 Sampling

1、SamplingChapter 7 Lecture 1Signals and Systems Spring 2015Homework # 57.1 7.2 7.3 7.6 7.9OutlineImpulse-train samplingReconstruction using interpolationNyquist sampling theoremSampling with a zero-order hold Sampling is a fundamental step to convert a CT signal to a DT signal.Consider a band limited

2、 signal , the FT of which is Employ an impulse train with period for sampling, whereImpulse Train SamplingThe samples of f(t) can be obtained as: sampling function: sampling period: sampling frequency: sampling angular frequencyHow to get the original signal f(t) from its sampled version y(t)?Equiva

3、lent problem: How to get F() from Y()?Reconstruction using interpolationHow to get the original signal f(t) from its sampled version y(t)?Equivalent problem: How to get F() from Y()?interpolation functionInterpolation is the inverse process of sampling.frequency spectrum aliasing (unwanted)Spectrum

4、AliasingNyquist Sampling TheoremNyquist rateWhen the sampling period satisfies Nyquistsampling theorem, we havesamplinglowpass filterExampleGiven a CT signal ,determine the Nyquist rates of following signals:(1) (2) (3)Solution: (1) The FT of is Using Nyquist sampling theorem,(2)(3)Zero-order hold i

5、s a LTI system, expressed asZero-Order Hold impulse-train samplingzero-order holdSampling With A Zero-Order HoldEach sampling value will be kept for , during which an A/D convertor can convert it to a digital signal.SamplingChapter 7 Lecture 2Signals and Systems Spring To recover , a reconstruction

6、filter is neededimpulse-train samplingzero-order holdreconstructionExample(1) Give the Nyquist rate of .(2) Sketch the spectrum of . (3) To reconstruct from , what condition should satisfy?(4) If , design a system to reconstruct from .Solution:(1) According to Nyquist sampling theorem(2) or(3) Using Nyquist sampling theoremor(4) Since , we haveEE4478: Digital Video Processing31儒效篇荀子曰:不聞不若聞之，聞之不若見(jiàn)之，見(jiàn)之不若知之，知之不若行之；學(xué)至于行之而止矣。Not hearing is not as good as hearing, hearing is not as good as seeing, seeing is not as good as mentally knowing, mentally knowing is not as good as acting; true le