通信原理3章答案.doc

3-4 (a)Show that an analog output waveform (which is proportional to the originalinput analog waveform) may be recovered from a naturally sampled PAM waveform by using the demodulation technique show in Fig.3-4.(b)Find the constant of proportionality, C , that is obtained with this demodulation technique ,where w(t) is the original waveform and Cw(t) is the recovered waveform. Note that C is a function of n, where the oscillator frequency is nfs.Solution:(a) Naturally sampled PAM： Demodulation: LPF after the LPF:(b) 另解：(a) after the LPF:(b) 3-9 An 850-Mbyte hard disk is used to store PCM data. Suppose that a voice-frequency (VF) signal is sampled at 8 ksamples/s and the encoded PCM is to have an average SNR of at least 30dB. How many minutes of VF conversation (i.e., PCM data) can be stored on the hard disk?Solution:3-10 An analog signal with a bandwidth of 4.2 MHz is to be converted into binary PCM and transmitted over a channel, The peak-signal quantizing noise ratio at the receiver output must be at least 55 dB. (a) If we assume that and that there is no ISI, what will be the word length and the number of quantizing steps needed?(b) What will be the equivalent bit rate?(c) What will be the channel null bandwidth required if rectangular pulse shapes are used?Solution:(a) (b) (c) For rectangular pulse shape3-11 Compact disk (CD) players use 16-bit PCM, including one parity bit with 8 times oversampling of the analog signal. The analog signal bandwidth is 20 KHz.(a) What is the null bandwidth of this PCM signal.(b) Using Eq.(3-18) , find the peak (SNR) in decibels.Solution:(a) for 8x oversampling of the recovered PCM signal (b) using (3-18)3-14 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 30dB. (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?Solution: (a) (b) The null bandwidth of the PCM signal is :3-17 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 , 20log(xrms/V) for (a) A PCM system that uses =10 law companding.(b) A PCM system that uses uniform quantization (no companding).Which of these systems is better to use in practice ? Why?Solution:(a) (b) 24 - law companding. =10 20 (dB) Uniform quantization (no companding). 10 -24 -20 -10 -4.77 0 (dB)A PCM system with - law companding is better to use in practice. Because that the output SNR is a function of the input level for the case of uniform quantization(no companding), but is relatively insensitive to the input level for - law companding .3-20 A multilevel digital communication system is to operate at a data rate of 9,600 bits/s.(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.Solution:(a) (b) 3-24 Consider a random data pattern consisting of binary 1s and 0s, where the probability of obtaining either a binary 1 or a binary 0 is . Calculate the PSD for the following types of signaling formats as a function of , the time needed to send 1 bit of data: (a) Polar RZ signaling where the pulse width is .(b) Manchester RZ signaling where the pulse width is . What is the first null bandwidth of these signals? What is the spectral efficiency for each of these signaling cases?Solution: (a) Tb f(t) 1 t 0Where the pulse shape, f(t), is shown in the figure, ThusThe first-null bandwidth is and the bandwidth efficiency is (bit/sec)/Hz. (b) Tb 1 f(t) 0 t -1Where the pulse shape, f(t), is shown in the figure, ThusThe first-null bandwidth is and the spectral efficiency is (bits/sec)/Hz.3-29 The data stream 01101000101 appears at the input of a differential encoder. Depending on the initial start-up condition of the encoder, find two possible differentially encoded data streams that can appear at the output.Solution:Input Sequence0 1 1 0 1 0 0 0 1 0 1Encoded Sequence(1) 11 0 1 1 0 0 0 0 1 1 0Encoded Sequence(2) 00 1 0 0 1 1 1 1 0 0 1 Reference digit 3-34 The information in an analog waveform is first encoded into binary PCM and then converted to a multilevel signal for transmission over the channel. The number of multilevels is eight. Assume that the analog signal has a bandwidth of 2,700Hz and is to be reproduced at the receiver output with an accuracy of % (full scale). (a) Determine the minimum bit rate of the PCM signal.(b) Determine the minimum baud rate of the multilevel signal.(c)Determine the minimum absolute channel bandwidth required for transmission of this PCM signal.Solution: (a) (b) (c) 3-45 An analog signal is to be converted into a PCM signal that is a binary polar NRZ line code. The signal is transmitted over a channel that is absolutely bandlimited to 4kHz. Assume that the PCM quantizer has 16 steps and that the overall equivalent system transfer function is of the raised cosine-rolloff type with r=0.5. (a) Find the maximum PCM bit rate that can be supported by this system without introducing ISI.(b) Find the maximum bandwidth that can be permitted for the analog signal.Solution:M=16=24n=4 (a) (b) 3-47 Multilevel data with an equivalent bit rate of 2,400 bits/s is sent over a channel using a four-level line code that has a rectangular pulse shape at the output of the transmitter. The overall transmission system (i.e., the transmitter, channel, and receiver) has an r=0.5 raised cosine-rolloff Nyquist filter characteristic