Signals and Systems - Electrical Engineering

0.3 Analog or Discrete? 11

FIGURE 0.5
Sampling an analog sinusoid
x(t)=2 cos( 2 πt), 0≤t≤ 10 , with two
different sampling periods,
(a)Ts 1 =0.1 secand (b)Ts 2 =1 sec, giving
x 1 (0.1n)andx 2 (n). The sinusoid is shown
by dashed lines. Notice the similarity
between the discrete-time signal and the
analog signal whenTs 1 =0.1 sec, while
they are very different whenTs 2 =1 sec,
indicating loss of information.

0 2 4

(a)

(b)

6 8 10

− 2

− 1

0

1

2

0 2 4 6 8 10

− 2

− 1

0

1

2

t(sec)

x^1

(0.1

n)

x^2

(n

)

FIGURE 0.6
Weekly closings of ACM stock for 160
weeks in 2006 to 2009. ACM is the trading
name of the stock of the imaginary
company, ACME Inc., makers of everything
you can imagine.

100

120

140

160

180

200

220

240

260

Dollars

ACM Closings, Jan. 2006−Dec. 2009

20 40 60 80 100 120 140

Week

As indicated before, not all signals are analog; there are some that are naturally discrete. Figure 0.6
displays the weekly average of the stock price of a fictitious company, ACME. Thinking of it as a signal,
it is naturally discrete-time as it does not come from the discretization of an analog signal.

We have shown in this section the significance of the sampling periodTsin the transformation of an analog

signal into a discrete-time signal without losing information. Choosing the sampling period requires knowl-

edge of the frequency content of the signal—this is an example of the relation between time and frequency to

be presented in great detail in Chapters 4 and 5, where the Fourier representation of periodic and nonperiodic