Digital Signals and Systems - Digital Signal Processing: Fundamentals and Applications - page 61

Table 3.2 Sample Values Calculated from the
Exponential Function
n

Þ n uðnÞ

10 ð 0 : 75

0 10 : 0000

1 7 : 5000

2 5 : 6250

3 4 : 2188

4 3 : 1641

5 2 : 3730

6 1 : 7798

7 1 : 3348

EXAMPLE 3.1
Sketch the following sequence

xðnÞ¼dðn þ 1Þþ0:5dðn 1Þþ2dðn 2Þ

Solution:
According to the shift operation, dðn þ 1Þ is obtained by shifting dðnÞ to the left by one sample, while dðn 1Þ and
dðn 2Þ are yielded by shifting dðnÞ to right by one sample and two samples, respectively. Using the amplitude of
each impulse function, we obtain the sketch in Figure 3.8 .

x ( n )

2

2

1

1

0.

n

3 2 1 0 1 2 3

FIGURE 3.8

Plot of digital sequence in Example 3.1.

3.1.2 Generation of Digital Signals
Given the sampling rate of a DSP system to sample the analytical function of an analog signal, the
corresponding digital function or digital sequence (assuming its sampled amplitudes are encoded to
have finite precision) can be found. The digital sequence is often used to
1. Calculate the encoded sample amplitude for a given sample number n .
2. Generate the sampled sequence for simulation.