Signal Processing and Linear Systems-B.P.Lathi copy

In all these cases instead of t ransmitting f t we t

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Unformatted text preview: in Fig. 5.11b. T he r esulting signal is a b inary P CM signal. T he analog signal f (t) is now converted t o a ( binary) digital signal. A b inary d igit is called b it for convenience. This contraction of binary digit by b it has become a n i ndustry s tandard a bbreviation. T he a udio signal b andwidth is a bout 15 kHz, b ut s ubjective tests show t hat signal a rticulation (intelligibility) is n ot affected if all t he c omponents above 3400 Hz a re suppressed. 3 t Since t he objective in telephone communication is intelligibility r ather t han h igh fidelity, t he c omponents above 3400 Hz are eliminated by a lowpass filter. T he r esulting signal is t hen s ampled a t a r ate o f 8000 samples per second (8 kHz). This r ate is i ntentionally kept higher t han t he Nyquist sampling r ate of 6.8 kHz t o avoid unrealizable filters required for signal reconstruction. Each sample is finally quantized into 256 levels (L = 256), which requires a group of eight binary pulses t o e ncode each sample (2 8 = 256). Thus, a digitized telephone signal consists o f 8 x 8000 = 64000 or 64 k bits/s d ata, requiring 64,000 b inary pulses p er second for its transmission. T he c ompact disc (CD) is a recent application of P CM. T his is a high-fidelity s ituation r equiring t he audio signal bandwidth of 15 kHz. Although t he Nyquist sampling r ate is only 30 kHz, a n a ctual sampling r ate of 44.1 kHz is used for the t Components b elow 300 Hz may also b e s uppressed w ithout affecting t he a rticulation. (a) Digit Binary equivalent Pulse code wavefonn 0 0000 I 0001 2 0010 • ••• • •• • 3 0011 4 0100 5 0101 6 0110 7 Olll 8 1000 9 1001 10 1010 11 1011 12 1100 13 1101 14 1110 15 l 1ll •• • • • • •• • ••• • ••• • •• • • • •• • • •• • •• • • ••• • ••• • • •• •• • • • •• • • ••• F ig. 5 .11 Analog-to-digital (A/D) conversion of a signal. (b) 334 5 Sampling reason mentioned earlier. T he signal is q uantized into a r ather large number of levels (L = 6 5,536) t o reduce quantizing error. T he binary-coded samples are now recorded on t he CD. Advantages o f Digital Signals Some o f t he advantages of digital signals over analog signals are listed below: 1. T ransmission of digital signals is more rugged t han t hat of analog signals because digital signals can withstand channel noise and distortion much b etter as long as t he noise a nd t he d istortion are within limits. T he digital (binary) message i n Fig. 5.12a is d istorted by t he channel, as illustrated in Fig. 5.12b. Yet if t he d istortion remains within a limit, we can recover t he d ata w ithout error because we need only t o make a simple binary decision as t o w hether the received pulse is positive o r negative. Figure 5.12c shows t he s ame d ata with channel d istortion a nd noise. Here again t he d ata can be recovered correctly as long as t he d istortion a nd t he noise are within limits. Such is n ot t he case with analog messages. Any distortion o r noise, no m atter how small, will distort the receive...
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