2006期末通信原理考题A及题解

学院_______________________ 系别____________ 班次_____________ 学号__________ 姓名________________………….……密…..……….封……..……线………..…以………..…内………....答…………...题…………..无…….….效…..………………..电子科技大学 2008 至 2009 学年 第 1 学期<< 通信原理 >> 课程考试题 (120分钟) 考试日期 2009 年 1 月 10 日1. (20 Points) Blank Filling:1) The three basic operations of the generation for PCM signal are __sampling_, ___quantizing__, __coding___.2) All communication systems involve three main subsystems: __Transmitter __ , channel and _Receiver __.3) If the analog signal is )1000042sin()(t t t s ππ+⨯=, the minimum sampling rate is _20kHz_. 4) If the data rate is 100kbps, the first null bandwidth for the unipolar NRZ signal, the polar NRZ signal and the Manchester NRZ signal are__100kHz___, __100kHz _, ___200kHz __ separately.5) For no ISI, and the 6 dB bandwidth of the raised cosine-rolloff filter, f 0, is designed to be 50kHz, the symbol rate of communication system is _100k _ baud.6) If the AM signal is )100002cos()]42cos(5.01[5)(t t t s ⨯⨯+=ππ, its complex envelope signal is _)]42cos(5.01[5)(t t g ⨯+=π_.7) Two main compression laws for non-uniform quantizing are: __u __-law, ___A__-law. 8) Assume that the input signals is0()[cos ][U(t)-U(t-T)] s t t t w =. When the input noise is white, the impulseresponse of the matched filter h(t)=___)]()())[(cos()(00000T t t U t t U t t t t +-----ω ___and the optimum sampling time =0t __T __.9) If the bandwidth of modulating signal is 50kHz, the transmission bandwidth for AM 、DSB-SC 、SSB 、signals are _100kHz__, __100kHz__, __200kHz__ separately.10) If the PSD of s(t) is []22222)4(12cos 16)(f T fT T A f b b b c g -=ππp2. (10 Points) Assume()m t is a unipolar NRZ signal occurring at a rate of 1000 bits/s (The peak valuesof which is 1V , and the probability of obtaining either a binary 1 or 0 is 1/2). The OOK signal is()()cos c c s t A m t t ω=, where 1c A V =.(a) Evaluate the PSD of the OOK signal. Assume a carrier frequency of 10 KHz. （4分）(b) Plot the PSD of the OOK （2分）signal and indicate the value of the first null-to-null bandwidth. （1分）(c) Evaluate the spectral efficiency for the OOK signal. （3分）Solution:(a) ()()cos c c s t A m t t ω= , m (t )为单极性 ()()c g t A m t =()sin ()()b b b b fT t f t F f T T fT ππ⎛⎫=↔= ⎪⎝⎭∏22:01,2210,2c n n kn For k A a a a and I +=⎧⎪⎪===⎨⎪⎪⎩依概率依概率222111(0)()0222cn n i i c i AR a a P A ===⨯+⨯=∑:0For k ≠,()[][][]24cn n k n n k AR k E a a E a E a ++===()22,02,04c c A k R k A k ⎧=⎪⎪=⎨⎪≠⎪⎩ ()()()222221()1()4111()()444sin sin sin c b g n bb c b bbA T n bP f f T T bA T T b b f f T bbfT fT fT fT fT fT δδδππππππ∞=-∞⎡⎤=+-⎢⎥⎣⎦⎡⎤=+=+⎢⎥⎣⎦⎛⎫∑⎪⎝⎭⎛⎫⎛⎫⎪ ⎪⎝⎭⎝⎭3311/1010b T R ms === ()()221()[()()]41()()16sin ()sin ()()()s g g c c b bc c P f P f f P f f c b c b T T f f f f c b c b f f T f f T f f T f f T δδππππ=-+--⎡⎤⎢⎥=++-++⎢⎥⎢⎥⎣⎦-+⎛⎫⎛⎫ ⎪ ⎪-+⎝⎭⎝⎭(b)2null B KHz =(c) 1/1//22null R Kb s b s Hz B KHz η===3. (10 Points) An analog signal with the bandwidth of 3400Hz is to be transmitted over a PCM system. The number of quantizing steps is 64. Assume the channel bandwidth is 15KHz. (a) Find the minimum sampling rate. （4分）(b) Determine the minimum bit rate required in the PCM signal. （3分）(c) Assume the overall equivalent system transfer function is of the raised cosine-rolloff type. When we use 4-level signal for sending data, is there ISI ？（3分）Solutiona.2234006800s f B Hz ==⨯=b.6466680040.8/s M n R nf Kb s=→===⨯=c. 20.42302channel RD KBd B KHz ==<= ()230115110.471220.4T T D B B r KHz r D =+=→=-=-=So, we can realizing zero ISI transmission.4. (10 Points) An modulated signal is described by the question ]2sin 102cos[100)(t f t f t s m c ππ+= where fc=10MHz, fm=1000Hz.(a) Evaluate the percentage of AM.(b) Assume that s(t) is an FM signal, find the frequency modulation index and the transmission bandwidth.(c) Assume that s(t) is a PM signal, find the peak phase deviation and the phase modulation index. (d) Assume that s(t) is fed into a 50-Ωload, evaluate the average power in the load.解：(a) 0(b) Hz dtt d F tf t m 10000})(max{212sin 10)(==∆=θππθ kHz f B f F m f T m f 221000)110(2)1(210100010000=⨯+=+===∆=ββ(c) 1010=∆==∆θβθP rad(d) W A P c 10050210050222=⨯=⨯=5. (10 Points) If the binary baseband signal is passed through a raised cosine-rolloff filter with 50% rolloff factor and is then modulated onto a carrier, the data rate is 32 kbits/s. Evaluate (a) The absolute bandwidth of resulting QPSK signal.(b) The approximate bandwidth of a resulting FSK signal when the mark frequency is 50 kHz and the space frequency is 60kHz. Solution:(a)(1)(1)22basebandD RB r r l=+=+ where 2=l for QPSK 320002(1)(10.5)242T basebandR B B r kHz l ==+=+=(b)1222()(1)T baseband B F B f f R r =∆+=-++(6000050000)32000(10.5)58kHz =-+⨯+=6. （10分）A binary data stream {1011010010100001001011} is transmitted using π/4 QPSK signal , and the first bit on the left is first passed into the multilevel system, the data rate is R. Assume the phase shift π/4 for 00, -π/4 for 01, +3π/4 for 10, -3π/4 for 11. Evaluate (a) calculate the carrier phase shift. （2.5分）(b) what is the minimum transmission bandwidth? （2.5分）(c) Assume the baseband signal is pass through a raised cosine-rolloff filter with a 50% rolloff factor first, what is the transmission bandwidth? （2.5分） (d) What is the spectrum efficiency? （2.5分） Solution:(a) The carrier phase shift isFrom the description of π/4 QPSK,use the table shown at the following:So the carrier phase is, assume the initial phase is 0(b) The minimum transmission bandwidth is:When the waveshape is sinc(x) type function, we can get the minimum transmission bandwidth02(1)24T r D RDR B r ===+=(c) Assume the baseband signal is pass through a raised cosine-rolloff filter with a 50% rolloff factor first, the transmission bandwidth is:0.523(1)28T r D RDR B r ===+=(d) The spectrum efficiency isFor (b) : 44TR RR B η===For (c) : 8338T R R R B η===7. (10 Points) The communication system is shown in the following figure, find the (S/N) for the receiver output.( ()cos 210m t π=⨯()out m t 10cos 210t ⨯n(t)Noise PSD 1mW/HzSolution:()10c o s c o s c s t ttω=Ω 23310/425221040002()210400082252 6.2588in T in T out inS W B Hz N f B W G S S G dB N N ϕ-===⨯⨯==⨯⨯=⨯⨯==⎛⎫⎛⎫==⨯=≈ ⎪ ⎪⎝⎭⎝⎭8. (10 Points) The digital receiver is shown in the following figure. Gaussian noise having a PSD of 1mW/Hz plus a polar signal with a peak level of A=10V is present at the receiver input. Find theexpression for BER as a function Q( ).Digital outputSolution:()010230010 102000 22200010425e s V s V N B Hz B W P Q Q Q σ-==-===⨯⨯====9. （10分）Suppose that the PSD of five digital transmission systems with bit rate of 1200bps are as following figures (a) to (e). Please answer the questions in the form below.。