ECE402 Continues-Time and Discrete-Time Signal

Sampling of Analog Signals

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Intended Learning Outcomes

Analyze the process of converting analog signals to digital signals.

Define sampling, quantization and coding. Solve related problems about ADC.

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Discrete - Time Sinusoidal Signal

1 = cos

6

Example:

Solution

= /6

0 =

2=

/6

2=

1

12 0 =

0

Therefore

0 = 12 = 1

Determine the fundamental period of the signal.

The fundamental period is 12 which corresponds to k=1 envelop cycle.

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Discrete - Time Sinusoidal Signal

1 = cos

6 Example: (cont.)

0 = 12 = 1

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Discrete - Time Sinusoidal Signal

1 = cos 8

31

Example:

Solution

= 8/31

0 =

2=

8/31

2=

4

31 0 =

0

Therefore

0 =31 = 4

Determine the fundamental period of the signal.

The fundamental period is 31 which corresponds to k=4 envelop cycle.

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Discrete - Time Sinusoidal Signal

1 = cos 8

31

Example: (cont.)

0 = 31 = 4

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Discrete - Time Sinusoidal Signal

Example: Determine whether or not each of the following signals is periodic. a. = cos 0.2

b. = cos20

140

c. = sin104

20

d. = cos

4

e. = cos 6

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Discrete - Time Sinusoidal Signal

Answer: a. 0 = 10, = 1, periodic b. 0 = 14, = 1, periodic c. 0 = 0.828, aperiodic d. 0 = 8, = 1,periodic e. 0 = 0.955, aperiodic

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