Page 332 - Satellite Communications, Fourth Edition

312 Chapter Ten

where v 0 is the output voltage normalized to the maximum output voltage, and
v i is the input voltage normalized to the maximum input voltage. The A-law
characteristic is given by

AZv i Z 1
v 0 sign(v i ) for 0 Zv i Z
1 ln A A

and

1 ln (AZv i Z) 1
v 0 sign(v i ) for Zv i Z 1
1 ln A A

10.4. Write down the expander transfer characteristics corresponding to the
compressor characteristics given in Prob. 10.3.

10.5. Assuming that the normalized levels shown in Fig. 10.4b represent
millivolts, write out the digitally encoded words for input levels of (a) 90 mV;
(b) 100 mV; (c) 190 mV; (d) 3000 mV.

10.6. Determine the decoded output voltage levels for the input levels given
in Prob. 10.5. Determine also the quantization error in each case.
10.7. (a) A test tone having the full peak-to-peak range is applied to a PCM
system. If the number of bits per sample is 8, determine the quantization S/N.
Assume uniform sampling of step size ΔV, for which the mean square noise
2
voltage is (ΔV) /12. (b) Given that a raised-cosine filter is used with 1,
determine the bandwidth expansion factor B/W, where B is the PCM bandwidth
and W is the upper cutoff frequency of the input.

10.8. A PCM signal uses the polar NRZ format. Following optimal filtering, the
[E b /N 0 ] at the input to the receiver decision detector is 10 dB. Determine the bit
error rate (BER) at the output of the decision detector.
10.9. Using Eq. (10.18), calculate the probability of bit error for [E b /N 0 ] values
of (a) 0 dB, (b) 10 dB, and (c) 40 dB.

10.10. A PCM system uses 8 bits per sample and polar NRZ transmission.
Determine the output [S/N] for [E b /N 0 ] values of (a) 0 dB, (b) 10 dB, and (c) 40 dB
at the input to the decision detector.

10.11. A binary periodic waveform of period 3T b is low-pass filtered before
being applied to a BPSK modulator. The low-pass filter cuts off at B 0.5/T b .
Derive the trigonometric expansion for the modulated wave, showing that only
side frequencies and no carrier are present. Given that the bit period is 100 ms
and the carrier frequency is 100 kHz, sketch the spectrum, showing the
frequencies to scale.