Chapter2 - CHAPTER 2: CHAPTER DISCRETE-TIME SIGNALS &...

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CHAPTER 2: CHAPTER 2: DISCRETE DISCRETE - - Lesson #4: DT signals Lesson #5: DT systems Lesson #6: DT convolution Lesson #7: Difference equation models Lesson #8: Block diagram for DT LTI systems Duration: 9 hrs
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Lecture #4 Lecture #4 DT signals DT signals 1. Representations of DT signals 2. Some elementary DT signals 3. Simple manipulations of DT signals 4. Characteristics of DT signals
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Converting a CT signal into a DT signal by sampling : given x a (t) to be a CT signal, x a (nT) is the value of x a (t) at t = nT b DT signal is defined only for n an integer < < = = n ), n ( x ) nT ( x ) t ( x a nT t a -2T -T 0 T 2T 3T 4T 5T 6T 7T . . . nT t Sampled signals Sampled signals
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n e -1 0 1 2 3 4 e x[n] e 0 0 1 4 1 0 e 1. Functional representation = = = n , 0 2 n , 4 3 , 1 n , 1 ] n [ x Representations of DT signals Representations of DT signals 2. Tabular representation
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3. Sequence representation Representations of DT signals Representations of DT signals { } 1 , 4 , 1 , 0 ] [ = n x -1 0 1 2 3 4 5 n 4. Graphical representation 4 1 1
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Lecture #4 Lecture #4 DT signals DT signals 1. Representations of DT signals 2. Some elementary DT signals 3. Simple manipulations of DT signals 4. Classification of DT signals
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1. Unit step sequence 2. Unit impulse signal 3. Sinusoidal signal 4. Exponential signal Some elementary DT signals Some elementary DT signals
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1 0 [ ] 0 0 n u n n , = , < Unit step Unit step -1 0 1 2 3 4 5 6 n 1 1 1
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Time Time - - shifted unit step shifted unit step < = 0 0 0 n n , 0 n n , 1 ] n n [ u 0 -n 0 -1 n 0 n 0 +1 n For n 0 > 0 1 1 1
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Time Time - - shifted unit step shifted unit step < = 0 0 0 n n , 0 n n , 1 ] n n [ u -n 0 -1 n 0 n 0 +1 0 n For n 0 < 0 1 1 1
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Unit impulse Unit impulse 1 0 [ ] 0 0 n n n δ , = = , -2 -1 0 1 2 n 1
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