Digital Signals and Systems - Digital Signal Processing: Fundamentals and Applications - page 58

x ( n )

x (0) x (1)

x (2)

......

3

n

-2 -1 0 1 2 4

x (3)

FIGURE 3.1

Digital signal notation.

xð 2 Þ : second sample amplitude at sample number n ¼ 2,
xð 3 Þ : third sample amplitude at sample number n ¼ 3, and so on.

Furthermore, Figure 3.2 illustrates the digital samples whose amplitudes are the discrete encoded
values represented in the digital signal (DS) processor. Precision of the data is based on the number of
bits used in the DSP system. The encoded data format can be either an integer if a fixed-point DS
processor is used or a floating-point number if a floating-point DP processor is used. As shown in
Figure 3.2 for the floating-point DS processor, we can identify the first five sample amplitudes at their
time indices as follows:
xð 0 Þ¼ 2 : 25
xð 1 Þ¼ 2 : 0
xð 2 Þ¼ 1 : 0
xð 3 Þ¼ 1 : 0
xð 4 Þ¼ 0 : 0
..
Again, note that each sample amplitude is plotted using a vertical bar with a solid dot. This notation is
well accepted in DSP literature.

3.1.1 Common Digital Sequences
Let us study some special digital sequences that are widely used. We define and plot each of them as
follows:
Unit-impulse sequence (digital unit-impulse function):

( 1

n ¼ 0

dðnÞ¼ (3.1)

0 n s 0

x ( n )

2.25 2.0

1.0

......
0 .0

3

n

-2 -1 0 1 2 4

FIGURE 3.2
Plot of the digital signal samples.