0195136047.pdf

658 SIGNAL PROCESSING

as alock-in amplifier.For extracting information from signals deeply buried in noise, more

sophisticated methods based on digital processing are available.

EXAMPLE 14.3.1

A low-noise transducer is connected to an instrumentation system by a cable that generates thermal

noise at room temperature. The information-bearing signal has a bandwidth of 6 kHz. The signal

power delivered isPin=120 pW. Evaluate the condition on the amplifier noise temperatureTa

such that the signal-to-noise ratio (SNR) is greater than or equal to 50 dB.

Solution

Applying Equation (14.3.10) withT=T 0 ,

SNR=

Pout

Nout

=

Pin

k(T+Ta)B

=

Pin

kT 0

(

1 +TTa 0

)

B

=

120 × 10 −^12

4 × 10 −^21

(

1 +TTa 0

)

6 × 103

≥ 105

Hence,

Ta≤ 49 T 0

This condition can easily be satisfied in the case of a well-designed amplifier.

14.4 Learning Objectives

Thelearning objectivesof this chapter are summarized here so that the student can check whether

he or she has accomplished each of the following.

• Basic ideas of analog and digital communication systems.


• Constructing the line spectrum of a periodic signal from its Fourier-series expansion.


• Conditions for distortionless transmission.


• Sketching spectra at various points in a system using product modulation and filtering.


• Conditions under which a signal can be sampled and then reconstructed from a pulse-
  modulated waveform.


• Basic notions of multiplexing systems.


• Causes of interference and noise, and techniques for minimizing their effects.

14.5 PRACTICAL APPLICATION: A CASE STUDY

Antinoise Systems—Noise Cancellation

Traditionally sound-absorbing materials have been used quite effectively to reduce noise levels in

aircraft, amphitheaters, and other locations. An alternate way is to develop an electronic system

that cancels the noise. Ear doctors and engineers have successfully developed ear devices that

will nearly eliminate the bothersome and irritating noise (so-called tinnitus) experienced by

patients suffering from Meni ́ `ere’s disease. For passengers in airplanes, helicopters, and other

flying equipment, a proper headgear is being developed in order to eliminate the annoying noise.