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Signals, Systems and Transforms: Matching Problems

Discrete-Time

Exercise 1

The diagrams show the impulse responses (Figure 1), frequency responses (Figure 2) and pole-zero diagrams (Figure 3) of 4 causal discrete-time LTI systems. But the diagrams are out of order. Match each diagram by filling out Table 1.

Impulse Response	Frequency Response	Pole-Zero Diagram
1
2
3
4

Figure 1:

Figure 2:

Figure 3: In these pole-zero diagrams, the zeros are shown with "o" and the poles are shown by "x".

Exercise 2

The diagrams show the impulse responses (Figure 4), frequency responses (Figure 5) and pole-zero diagrams (Figure 6) of 4 causal discrete-time LTI systems. But the diagrams are out of order. Match each diagram by filling out Table 2.

Impulse Response	Frequency Response	Pole-Zero Diagram
1
2
3
4

Figure 4:

Figure 5:

Figure 6: In these pole-zero diagrams, the zeros are shown with "o" and the poles are shown by "x".

Exercise 3

The diagrams show the impulse responses (Figure 7) and pole-zero diagrams (Figure 8) of 8 causal discrete-time LTI systems. But the diagrams are out of order. Match each diagram by filling out Table 3.

Impulse Response	Pole-Zero Diagram
1
2
3
4
5
6
7
8

Figure 7:

Figure 8: In these pole-zero diagrams, the zeros are shown with "o" and the poles are shown by "x".

Exercise 4

The diagrams show the frequency responses magnitudes |Hfω| H ω f (Figure 9) and pole-zero diagrams (Figure 10) of 8 causal discrete-time LTI systems. But the diagrams are out of order. Match each diagram by filling out Table 4.

Frequency Response	Pole-Zero Diagram
1
2
3
4
5
6
7
8

Figure 9:

Figure 10: In these pole-zero diagrams, the zeros are shown with "o" and the poles are shown by "x".

Exercise 5

The diagrams show the frequency responses (Figure 11), impulse responses (Figure 12), and pole-zero diagrams (Figure 13) of 4 causal discrete-time LTI systems. But the diagrams are out of order. Match each diagram by filling out Table 5.

Frequency Response	Pole-Zero Diagram	Impulse Response
1
2
3
4

Figure 11:

Figure 12:

Figure 13: In these pole-zero diagrams, the zeros are shown with "o" and the poles are shown by "x".

Exercise 6

The diagrams show the frequency responses (Figure 14) and pole-zero diagrams (Figure 15) of 6 causal discrete-time LTI systems. But the diagrams are out of order. Match each diagram by filling out Table 6.

Frequency Response	Pole-Zero Diagram
1
2
3
4
5
6

Figure 14:

Figure 15: In these pole-zero diagrams, the zeros are shown with "o" and the poles are shown by "x".

Exercise 7

The diagrams show the pole-zero diagrams (Figure 16) and impulse responses (Figure 17) of 8 causal discrete-time LTI systems. But the diagrams are out of order. Match each diagram by filling out Table 7.

Pole-Zero Diagram	Impulse Response
1
2
3
4
5
6
7
8

Figure 16: In these pole-zero diagrams, the zeros are shown with "o" and the poles are shown by "x".

Figure 17:

Continuous-Time

Exercise 8

Match the impulse response ht h t of a continuous-time LTI system with the correct plot of its frequency response |Hfω| H ω f . Explain how you obtain your answer.

Figure 18:

Figure 19:

Exercise 9

For the impulse response ht h t illustrated in Figure 18, identify the correct diagram of the poles of Hs H s . Explain how you obtain your answer.

Figure 20:

Exercise 10

Figure 21 indicate the pole locations of six continuous-time LTI systems. Match each with the corresponding impulse response (Figure 22) without actually computing the Laplace transform.

Pole-Zero Diagram	Impulse Response
1
2
3
4
5
6

Figure 21:

Figure 22:

Exercise 11

Figure 23 shows the impulse responses and frequency responses of four continuous-time LTI systems. But they are out of order. Match the impulse response to its frequency response magnitude, and explain your answer.

Impulse Response	Frequency Response
1
2
3
4

Figure 23:

Exercise 12

Figure 24 shows the impulse responses and frequency responses of four continuous-time LTI systems. But they are out of order. Match each impulse response with its frequency response.

Impulse Response	Frequency Response
1
2
3
4

Figure 24:

Exercise 13

Figure 25 shows the pole diagrams and frequency responses of four continuous-time LTI systems. But they are out of order. Match each pole diagram with its frequency response.

Pole Diagram	Frequency Response
1
2
3
4

Figure 25:

Exercise 14

The diagrams show the pole-zero diagrams (Figure 26) and frequency responses (Figure 27) of 8 causal discrete-time LTI systems. But the diagrams are out of order. Match each diagram by filling out Table 12.

Pole-Zero Diagram	Frequency Response
1
2
3
4
5
6
7
8

Figure 26: In these pole-zero diagrams, the zeros are shown with "o" and the poles are shown by "x".

Figure 27:

Exercise 15

The figures show two input signals x 1 t x 1 t and x 2 t x 2 t , two impulse responses h 1 t h 1 t and h 2 t h 2 t (see Figure 28), and four output signals y 1 t y 1 t , y 2 t y 2 t , y 3 t y 3 t , y 4 t y 4 t (see Figure 29). Identify which input signal and which impulse response causes each of the four output signals. (Your answer should have four parts; y 1 t= h ? t* x ? t y 1 t h ? t x ? t , etc.)

Figure 28:

Figure 29:

Exercise 16

The figures show two input signals x 1 t x 1 t and x 2 t x 2 t , two impulse responses h 1 t h 1 t (see Figure 30) and h 2 t h 2 t , and four output signals y 1 t y 1 t , y 2 t y 2 t , y 3 t y 3 t , y 4 t y 4 t (see Figure 31). Identify which input signal and which impulse response causes each of the four output signals. (Your answer should have four parts; y 1 t= h ? t* x ? t y 1 t h ? t x ? t , etc.)

Figure 30:

Figure 31:

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Last edited by Charlet Reedstrom on Nov 4, 2004 2:45 pm US/Central.

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