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1.+Further+Study+of+Sampling

1.+Further+Study+of+Sampling - 1 Further Study of Sampling...

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1. Further Study of Sampling 1.1. Implementation of Continuous-Time Systems by Discrete-Time Systems (4.4) 1.2. Implementation of Discrete-Time Systems by Continuous-Time Systems (4.5) 1.3. Changing Sampling Interval Using Only Discrete-Time Operations (4.6)

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1.1. Implementation of Continuous-Time Systems by Discrete- Time Systems A continuous-time system can be implemented by a discrete-time system (figure 1.1). x c (t) Figure 1.1. Implementation of a Continuous- Time System by a Discrete-Time System. C/D DTS D/C Example. An ideal low-pass discrete-time filter has the frequency response x(n) y(n) y c (t) T T, 0
x c (t) C/D H( ) D/C x(n) y(n) y c (t) T T Figure 1.2. An Ideal Low-Pass Continuous-Time Filter Implemented by an Ideal Low-Pass Discrete-Time Filter.  /T /T X c ( ) A 0 Figure 1.3. Continuous-Time Fourier Transform of x c (t).

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(1.1) 0 0 | | 0, | | , 1 ) H( over period [  , ). As shown in figure 1.2, this system can be used to implement an ideal low-pass continuous-time filter. Assume that
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