Signals and Systems - Electrical Engineering

1.3 Continuous-Time Signals 69

0 2 4 6 8 10

− 1

−0.8

−0.6

−0.4

−0.2

0

0.2

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0.8

1

(a)

t(sec)

v(

t)

1.45 1.5 1.55

−0.5

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−0.3

−0.2

−0.1

0

0.1

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(b)

t, nTs

v(

t),

v(

nT

)s 1.45 1.5 1.55

−0.5

0

0.5

(d)

(c)

v(

nT

), s

vq

(nT

)s

1.45 1.5 1.55

−0.5

0

0.5

nTs

e(

nT

)s

FIGURE 1.2
(a) A segment of this speech signal is sampled and quantized. (b) The speech segment (continuous line) and
the sampled signal (vertical samples) using a sampling periodTs= 10 −^3 sec.(c) The sampled and the
quantized signal. (d) The quantization error (that is, the difference between the sampled and the quantized
signals) is shown.

Thus, the independent variable is timet, and the value of the function at some timet 0 ,x(t 0 ), is a real (or a

complex) value. (Although in practice signals are real, it is useful in theory to have the option of complex-

valued signals.) It is assumed that both timetand signal amplitudex(t)can vary continuously, if needed, from

−∞to∞.

The termanalogused for continuous-time signals derives from the similarity of acoustic signals to the
pressure variations generated by voice, music, or any other acoustic signal. The termscontinuous-time
andanalogare used interchangeably for these signals.