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Baseband Pulse and Digital Signaling Chap. 3
★ 3–16 In a PCM system, the bit error rate due to channel noise is 10 -4 . Assume that the peak signal-to-noise
ratio on the recovered analog signal needs to be at least 30 dB.
(a) Find the minimum number of quantizing steps that can be used to encode the analog signal
into a PCM signal.
(b) If the original analog signal had an absolute bandwidth of 2.7 kHz, what is the null bandwidth
of the PCM signal for the polar NRZ signaling case?
3–17 Referring to Fig. 3–20 for a bit synchronizer using a square-law device, draw some typical waveforms
that will appear in the bit synchronizer if a Manchester encoded PCM signal is present at
the input. Discuss whether you would expect this bit synchronizer to work better for the
Manchester encoded PCM signal or for a polar NRZ encoded PCM signal.
3–18 (a) Sketch the complete µ = 10 compressor characteristic that will handle input voltages over the
range -5 to +5 V.
(b) Plot the corresponding expandor characteristic.
(c) Draw a 16-level nonuniform quantizer characteristic that corresponds to the µ = 10 compression
characteristic.
3–19 For a 4-bit PCM system, calculate and sketch a plot of the output SNR (in decibels) as a function
of the relative input level, 20 log (x rms V) for
(a) A PCM system that uses µ = 10 law companding.
(b) A PCM system that uses uniform quantization (no companding).
(c) Which of these systems is better to use in practice? Why?
★ 3–20 The performance of a µ = 255 law companded PCM system is to be examined when the input
consists of a sine wave having a peak value of V volts. Assume that M = 256.
(a) Find an expression that describes the output SNR for this companded PCM system.
(b) Plot (SN) out (in decibels) as a function of the relative input level, 20 log (x rms V). Compare
this result with that shown in Fig. 3–10.
3–21 A multilevel digital communication system sends one of 16 possible levels over the channel every
0.8 ms.
(a) What is the number of bits corresponding to each level?
(b) What is the baud rate?
(c) What is the bit rate?
3–22 In the United States, HDTV stations transmit on-the-air eight-level RF (radio frequency) signals
(see Sec. 8–9). If the baud (symbol) rate for these signals is 10.76 Msymbolss, calculate the
effective bit rate for these transmitted signals.
3–23 A multilevel digital communication system is to operate at a data rate of 1.5 Mbs.
(a) If 4-bit words are encoded into each level for transmission over the channel, what is the minimum
required bandwidth for the channel?
(b) Repeat part (a) for the case of 8-bit encoding into each level.
★ 3–24 Consider a deterministic test pattern consisting of alternating binary 1’s and binary 0’s.
Determine the magnitude spectra (not the PSD) for unipolar NRZ signaling as a function of T b ,
the time needed to send one bit of data. How would the magnitude spectra change if the test
pattern was changed to an alternating sequence of four 1’s followed by four binary 0’s?
★ 3–25 Rework Prob. 3–24 for the case of unipolar RZ signaling where the pulse width is t = 3 4 T b.
3–26 Consider a random data pattern consisting of binary 1’s and 0’s, where the probability of
1
obtaining either a binary 1 or a binary 0 is 2 . Calculate the PSD for unipolar NRZ signaling as
a function of T b , the time needed to send one bit of data.