0195136047.pdf

714 COMMUNICATION SYSTEMS

(

So

Nq

)

=

3 L^2

KCR^2

(15.3.9)

It can be seen that messages with large crest factors will lead to poor performance.

Companding

In order to lower the crest factor of a waveform, so as to produce better performance, a process

known ascompandingis used. It works like acompressorwhich progressively compresses the

larger amplitudes of a message when it is passed through a nonlinear network. The inverse

operation in the receiver is known as anexpandor,when it restores the original message. Figure

15.3.4 illustrates a typical set of input–output characteristics for a form of compandor. One can see

that the action of the compressor is to increase the rms–signal value for a given peak magnitude.

Source Encoding

After the quantization of message samples, the digital system will then code each quantized

sample into a sequence of binary digits (bits) 0 and 1. Using thenatural binary codeis a simple

approach. For a code withNbbits, integersN(from 0 to 2Nb−1) are represented by a sequence

of digits,bNb,bNb− 1 ,...,b 2 ,b 1 , such that

N=bNb( 2 Nb−^1 )+...+b 2 ( 21 )+b 1 ( 20 ) (15.3.10)

Note thatb 1 is known as the least significant bit (LSB), andbNbas the most significant bit (MSB).

Since a natural binary code ofNbbits can encodeLb= 2 Nblevels, it follows that

|f(t)|max

|f(t)|max

|f(t)|max

|f(t)|max

Input

Input

No compression

With compression

No expansion

With expansion

Output

Output

(a)

(b)

Figure 15.3.4Compandor input–output character-

istics.(a)Compressor.(b)Expandor.