PROBLEMS 659
Applications could conceivably extend to people residing near airports and bothered by airplane
takeoffs and landings. For industrial workers who are likely to develop long-term ill effects due
to various noises they may be subjected to in their workplace, and even for persons who are
irritated by the pedestrian noise levels in certain locations, antinoise systems that nearly eliminate
or nullify noise become very desirable.
Figure 14.5.1 illustrates in block-diagram form the principle of noise cancellation as applied
to an aircraft carrying passengers. The electric signal resulting after sampling the noise at the
noise sources is passed through a filter whose transfer function is continuously adjusted by a
special-purpose computer to match the transfer function of the sound path. An inverted version
of the signal is finally applied to loudspeakers, which project the sound waves out of phase with
those from the noise sources, nearly canceling the noise. Microphones on the headrests monitor
the sound experienced by the airline passengers so that the computer can determine the proper
filter adjustments.
Signal processing, which is concerned with manipulating signals to extract information and
to use that information to generate other useful electric signals, is indeed an important and far-
reaching subject.
Adaptable
filter
Computer
Noise
source
Microphone near
sources of noise
such as
engines and propellers
(noise sampled before
entering passenger area)
Microphones
(located on passenger headrests)
monitor sound level
Inverted signal version
of the transfer function
of the sound path
applied to loudspeakers
Sound waves
nearly cancel those
from noise sources
Loudspeakers
located in
passenger
cabin area
Figure 14.5.1Block diagram of antinoise system to suppress the noise in an aircraft.
Problems
14.1.1(a) A rectangular pulse is denoted by(t)and
defined as
(t)=
1 , −
1
2
<t<
1
2
1
2 ,t=±
1
2
0 , otherwise
Sketch the signal. Also express it in terms of
unit-step signals.
(b) The sinc signal is given by
sinc(t)=
{sinπt
πt,t=^0
1 ,t= 0
Sketch the waveform and comment on its
salient features.
(c) The sign or signum signal is represented by
