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Chapter: 10 -Problem: 13 >> (a) Using (10.93) and appropriate bounds for PE,symbol, obtain Eb / N0 required for achieving PE,bit = 10-4 for M-ary PSK with M = 8, 16, 32.(b) Repeat for QAM for the same M values using (10.63).
Answer Preview: a The bounds on symbol error probability are given by P 1 P E symbol 2P 1 wher…

, What are two gross characterizations of the type of multi path typically found in cellular radio systems.
Answer Preview: RF signals transmitted via wireless mobile channels suffer from several effects like small- scale fa…

, Chapter: 2 -Problem: 18 >> Obtain the complex exponential Fourier series coefficients for the (a) pulse train, (b) half-rectified sinewave, (c) full-rectified sinewave, and (d) triangular waveform as given in Table 2.1. Transcribed Image Text: Table 2.1 Fourier Series for Several Periodic Signals Signal (one period) Coefficie
Answer Preview: This is a matter of integration Only the solution for part b will be given here The integral …

, What two sources of noise affect the convergence of a tap weight adjustment algorithm for an equalizer?
Answer Preview: Angle random walk (ARW) is the noise component at the output of a fibe…

, Chapter: 2 -Problem: 25 >> (a) Use the Fourier transform of x(t) = exp (-αt) u (t) - exp (αt) u (-t) where α > 0  (b) Use the result above and the relation u(t) = 1/2[sgn (t) + 1] to find Fourier transform of the unit step.(c) Use the integration theorem and the Fourier transform of the unit impulse function to find the Fourier transform of the unit step. Compare the result with part (b).
Answer Preview: a Using a table of Fourier transforms and the time reversal theorem the Fourier transf…

, Chapter: 8 -Problem: 8 >> The threshold level for an envelope detector is sometimes defined as that value of (SNR)T for which Ac > rn with probability 0.99. Assuming that a2m?2n ? 1, derive the SNR at threshold, expressed in decibels.
Answer Preview: The output of the predetection filter is e t A c 1 am n t cos w c t r n t co…

, White Gaussian noise of double-sided power spectral density 1 W/Hz is passed through a filter with frequency response function H(f) = (1 +j2?f)-1.(a) What is the power spectral density, SY(f), of the output process?(b) What is the auto correlation function, RY (?), of the output process?(c) What is the mean of the output process? (d) What is the variance of the output process? (e) Is the output pr
Answer Preview: (a) The power spectral density of the output process is given by: SY(f) = |H(f)|^2 * Sx(f) where Sx(…

, Chapter: 3 -Problem: 17 >> Squaring a DSB or AM signal generates a frequency component at twice the carrier frequency. Is this also true for SSB signals? Show that it is or is not.
Answer Preview: We have which is or Therefor…

, Chapter: 9 -Problem: 22 >> (a) Consider the transmission of digital data at a rate of R = 50 kbps and at an error probability of PE = 10-6. Using the bandwidth of the main lobe as a bandwidth measure, give an estimate of the required transmission bandwidth and Eb / N0 in decibels required for the following coherent modulation schemes:(i) binary ASK; (ii) BPSK; (iii) binary coherent FSK (take the minimum spacing possible bet
Answer Preview: a For BPSK an SNR of 10 53 dB is required to give an error probability of 10 6 see the solution to P…

, The input to a receiver has a signal component having the PSD SS(f) = 5?(f/7). The noise component is (10-4) II(f/20). Determine the SNR in dB.
Answer Preview: The autocorrelation function and the rate of change Consider a WSS random …

, Chapter: 2 -Problem: 68 >> Figure 2.41 illustrates so-called zero-order-hold reconstruction.(a) Sketch y(t) for a typical x(t). Under what conditions is y(t) a good approximation to x(t)?(b) Find the spectrum of y(t) in terms of the spectrum of x(t). Discuss the approximation of y(t) to x(t) in terms of frequency-domain arguments. Transcribed Image
Answer Preview: a The sampling frequency should be large com…

, Chapter: 8 -Problem: 11 >> Verify the correctness of (8.59). Transcribed Image Text: = E {Ir?t) + n?t»F} – E²in?u) + n?t»)l = 4c; (8.59) ?+n?
Answer Preview: Equation 8 59 is suppressing t The first …

, A communications system operates with a message signal bandwidth of 10 kHz and a transmission bandwidth of 250 kHz. What is the bandwidth expansion factor? Assuming a pre-detection SNR of 20 dB and optimum demodulation, determine the post detection SNR.
Answer Preview: Bw = 10kHz - 250kHz = 0 1utte…

, Chapter: 2 -Problem: 14 >> Find the energies and powers of the following signals (note that 0 and ˆž are possible answers). Tell which are energy signals and which are power signals.(a) x1(t) = cos(10Ï€t) u(t) u(2 - t)(b)(c) x3(t) = e-|t| cos (2Ï€t)(d) x4(t) = II (t/2) + Δ (t) Transcribed Image Text: X ()?? 1-3? 2 x,(t) = 2=
Answer Preview: a This is a cosine burst nonzero between 0 and 2 seconds Its power is 0 …

, Give advantages and disadvantages of the carrier modulation methods illustrated in Figure 5.19. Figure 5.19 Transcribed Image Text: Data ASK PSK FSK
Answer Preview: 1 1 Advantages of ASK -; 1) It offers high bandwidth efficiency. 2) It has simple receiver design. 3) ASK modulation can be used to transmit digital d…

, Chapter: 4 -Problem: 5 >> Compute the single-sided amplitude and phase spectra of xc3 (t) = A sin[2Ï€fct + β sin(2Ï€fmt)]and xc4 (t) = Ac sin[2Ï€fct + Î² cos(2Ï€fmt)]Compare the results with Figure 4.5. Figure 4.5 Transcribed Image Text: AL2(B)| AHo($)] AV¿(B[ AV4B)| AdL3(B)| AV_4(B)| f (a) (b) Phase, rad Amplitude " -s fe-
Answer Preview: Since sin x cos x 2 we can write which is x c3 t A C R…

, Which data formats, for a random (coin toss) data stream, have (a) zero dc level; (b) built in redundancy that could be used for error checking; (c) discrete spectral lines present in their power spectra; (d) nulls in their spectra at zero frequency; (e) the most compact power spectra (measured to first null of their power spectra)? (i) NRZ change; (ii) NRZ mark; (iii) Unipolar RZ; (iv) Polar RZ;
Answer Preview: Here is a summary of the characteristics you listed for the different data formats a Zero DC level NRZ change NRZ mark Unipolar RZ Polar RZ Bipolar RZ b Built in redundancy for error checking Split ph…

, A message occurs with a probability of 0.8. Determine the information associated with the message in bits, nats, and hartleys.
Answer Preview: 1) Information in bits I(X) = - log 2 P(X) bits I(X) = - log 2 (…

, Chapter: 4 -Problem: 27 >> Verify (4.120) by showing that Kte - Kttu(t) satisfies all properties of an impulse function in the limit as Kt ? ?.
Answer Preview: From the definition f t K t e K t t u t it is c…

, Chapter: 2 -Problem: 35 >> Obtain and sketch the convolutions of the following signals.(a) y1(t) = e-atu(t) ? Il(t - ?), a and ? positive constants(b) y2(t) = [II(t/2) + II(t)] ? Il(t)(c) y3(t) = e-?|t| ? II(t), a > 0 (d) y4 (t) = x(t) ? u (t), where x(t) is any energy signal [you will have to assume a particular form for x(t) to sketch this one, but obtain the general result before doing so].
Answer Preview: a The convolution operation gives b The convolution of these two signals gi…

, Chapter: 11 -Problem: 33 >> Consider the reception of a BPSK signal in noise with unknown phase, θ, to be estimated. The two hypotheses may be expressed asH1 : y(t) = A cos(ωct + θ) + n(t), 0 ‰¤ t ‰¤ TsH2 : y(t) = -A cos(ωct + θ) + n(t), 0 ‰¤ t ‰¤ Tswhere A is a constant and n(t) is white Gaussian noise with single-sided power spectral density N0, and the hypotheses are equally probable [P(H1) = P(H2)].(a) Using Ï•1 and
Answer Preview: a Use the basis function set and trigonometric expansion of the received data as H 1 yt A cos cos c …

, How many total samples of the incoming pulse are required to force the following number of zeros on either side of the middle sample for a zero-forcing equalizer? (a) 1;(b) 3;(c) 4;(d) 7;(e) 8;(f) 10.
Answer Preview: Rescuers should phone first for unresponsive adults. Exceptions: phone fast (provide CPR first) for …

, Chapter: 2 -Problem: 11 >> Find the powers of the following periodic signals. In each case provide a sketch of the signal and give its period.(a) x1 (t) = 2 cos (4Ï€t - Ï€/3)(b) (c) (d)  Transcribed Image Text: t-4? x, ()-?3? n=-00 2 t-6? x, ()??? 1-0?
Answer Preview: a Using the fact that the power contained in a sinusoid is its a…

, Chapter: 9 -Problem: 4 >> A receiver for base band digital data has a threshold set at ? instead of zero. Rederive (9.8), (9.9), and (9.11) taking this into account. If P(+A) = P(-A) = 1/2, find Eb / N0 in decibels as a function of e for 0 ? ? /? ? 1 to give PE = 10-6, where ?2 is the variance of N.
Answer Preview: The decision criterion is V choose A V choose A where V AT N N is a Gaussia…

, A 10,000 ohm resistor operates at a temperature of 290 K. Determine the variance of the noise generated in a bandwidth of 1,000,000 Hz.
Answer Preview: As we know that the formula for varience noise =kBT Where K = boltmanz constant B = bandwi…

, Chapter: 3 -Problem: 11 >> An AM modulator has outputxc(t) = A cos[2?(200)t] + B cos[2?(180)t] +B cos[2?(220)t]The carrier power is P0 and the efficiency is Eff. Derive an expression for Eff in terms of P0, A, and B. Determine A,B, and P0 = 200 W and Eff = 30%.
Answer Preview: The side band power is The efficiency is The carrier power …

, Chapter: 2 -Problem: 34 >> Evaluate the following integrals using Rayleigh€™s energy theorem (Parseval€™s theorem for Fourier transforms). (a) (b) (c) (d) Transcribed Image Text: I = L 00 a2+(2xf )² -? I, = [ sinc 2(7 f)df 00 %3D
Answer Preview: a Use the transform pair Using Rayleighs energy theorem we obtai…

, Chapter: 9 -Problem: 6 >> Write a computer program to verify Figures 9.28 and 9.29. Figure 9.28 Figure 9.29 Transcribed Image Text: T'm = T 10-1 10-2 8 =-0.6 8= -0.9 T', = 1 T'm = 0 , =0 10-3 T'm = 1 8 =-0.3 T'm = 0 T'm = 1 8 = 0.6 T'm = 1 8 = 0.3 Tm = 1 8 = 0.9 T'm = 1 10-4 8 = 0.9; 6 = 0.6; 8 = 0.3: 6 = 0 T'm =0 Tm=0 m=0 F
Answer Preview: clf z0dB 0 1 30 z0 10 z0dB 10 for delta 0 9 0 3 0 6 if delta eps …

, While free-space propagation of electromagnetic waves is typically characterized by an inverse square-law decrease in power density with distance from the source, what is the range of power law decrease for cellular radio? Explain why the difference from free-space propagation.
Answer Preview: The free space propagation model is used to predict received signal strength when the transmitter an…

, Chapter: 3 -Problem: 13 >> An AM modulator is operating with an index of 0.8. The modulating signal ism(t) = 2 cos(2?fmt) + cos(4?fmt) + 2 cos(10?fmt)(a) Sketch the spectrum of the modulator output showing the weights of all impulse functions. (b) What is the efficiency of the modulation process?
Answer Preview: a By plotting m t or by using a root finding algor…

, Chapter: 2 -Problem: 42 >> Find the auto correlation functions of the signals having the following power spectral densities. Also give their average powers.(a) S1 (f) = 4? (f - 15) + 4? (f + 15)(b) S2 (f) = 9? (f - 20) + 9? (f + 20)(c) S3 (f) = 16? (f - 5) + 16? (f + 5)(d) S4 (f) = 9? (f - 20) + 9? (f + 20) + 16? (f - 5) + 16? (f + 5)
Answer Preview: Since the auto correlation function and power spectral density of a signal are F…

, The input signal to a matched filter is given by The noise is white with signal-sided power spectral density N0 = 10-1 W/Hz. What is the peak signal-squared-to-mean-square-noise ratio at its output? Transcribed Image Text: ( 2, 0 <1 < 1 g (t) = { 1, 1
Answer Preview: The peak signal-squared-to-mean-square-noise ratio …

, Chapter: 3 -Problem: 10 >> An AM modulator has outputxc (t) = 40 cos [20?(200)t] + 5 cos[2?(180)t] + 5 cos[2?(220)t]Determine the modulation index and the efficiency.
Answer Preview: The modulator output x c t 40 cos 20 200 t 5 cos 2 180 t 5 cos 2 220 t can be writte…

, Chapter: 2 -Problem: 39 >> Provide plots of the following functions of time and find their Fourier transforms. Tell which ones should be real and even functions of f and which ones should be imaginary and odd functions of f. Do your results bear this out?(a) (b) (c) (d) x4 (t) = Λ (t - 1) - Λ (t + 1)(e) x5 (t) = Λ (t) sgn(t) (f) x6 (t) = Λ (t) cos (2Ï€t)
Answer Preview: Signals x 1 t x 2 t and x 6 t are real and even Therefore their Fourier transfor…

, Chapter: 9 -Problem: 4 >> Write a computer program to evaluate various digital modulation techniques: (a) For a specified data rate and error probability, find the required bandwidth and Eb / N0 in decibels. Corresponding to the data rate and required Eb / N0, find the required received-signal power for N0 = 1 W/Hz.(b) For a specified bandwidth and error probability find the allowed data rate and required Eb / N0 in decibe
Answer Preview: ce94 For a given data rate and error probability find the required bandwidth and EbN0 in dB baseband BPSKDPSK coherent FSK and noncoherent FSK modulat…

, Referring to the circuit of Figure A.8, consider RL to be a load resistance, and find it in terms of R1, R2, and R3 so that the maximum available noise power available from R1, R2, and R3 is delivered to it. Transcribed Image Text: R2 - RL R3 R1
Answer Preview: Maximum power will be delivered to load resistance when the l…

, Chapter: 3 -Problem: 23 >> A DSB signal is squared to generate a carrier component that may then be used for demodulation. (A technique for doing this, namely the phase-locked loop, will be studied in the next chapter.) Derive an expression that illustrates the impact of interference on this technique.
Answer Preview: We assume single tone interference as in the body of th…

, Chapter: 8 -Problem: 18 >> Draw a phasor diagram for an angle-modulated signal for (SNR)T >> 1 illustrating the relationship between R(t), Ac, and rn(t). Show on this phasor diagram the relationship between ?(t), ?(t) and ?n(t). Using the phasor diagram, justify that for (SNR)T >> 1, the approximation?(t) ? ?(t) + rn(t) / Ac sin[?n(t) - ?(t)]is valid. Draw a second phasor diagram for the case in which (SNR)T << 1 and show t
Answer Preview: The phasor diagram for SNR 1 is illustrated in Figure 8 4 The phasor diagram f…

, Obtain an expression for F and Te for the two-port resistive matching network shown in Figure A.10, assuming a source at T0 = 290? K. Transcribed Image Text: R1 R2
Answer Preview: F = (R1 / (R1 + R2))^2 Te = (T0 - (R1/ (R1 + R2))^2 * T0) / (1 - (R1/ (R1 + R2))^2) Explanation: To …

, Chapter: 4 -Problem: 4 >> We previously computed the spectrum of the FM signal defined by xc1 (t) = Ac cos[2?fct + ? sin(2?fmt)]Now assume that the modulated signal is given byxc2 (t) = Ac cos[2?fct + ? cos(2?fmt)]Show that the amplitude spectrum of xc1 (t) and xc2 (t) are identical. Compute the phase spectrum of xc2 (t) and compare with the phase spectrum of xc1(t).
Answer Preview: Let t cos m t where m 2f m This gives x c2 t A C Re e …

, Referring to Drill Problem 6.2, find the following:(a) P(A|B);(b) P(B|A); Data From Problem 6.2In tossing a six-sided fair die, we define event A = {2 or 4 or 6} and event B = {1 or 3 or 5 or 6}. Using equal likelihood and the axioms of probability, find the following: (a) P(A);(b) P(B);(c) P(A ? B);(d) P (A ? B);(e) P (A | B);(f) P (B |A);
Answer Preview: Probability of an event E is denoted as P(E) = ( Number of favourable outcomes ) / ( Tota…

, Chapter: 4 -Problem: 16 >> By making use of (4.30) and (4.39), show that Transcribed Image Text: ?0 ?)-1 n=-00
Answer Preview: From we obtain Also x 2 c t A 2 …

, Chapter: 2 -Problem: 67 >> A flat-top sampler can be represented as the block diagram of Figure 2.40. (a) Assuming Ï„ << Ts, sketch the output for a typical x(t).(b) Find the spectrum of the output, Y(f), in terms of the spectrum of the input, X(f). Determine the relationship between Ï„ and Ts required to minimize distortion in the recovered waveform?.
Answer Preview: a The leading edges of the at top samples follow the waveform at the sampl…

, Chapter: 8 -Problem: 17 >> Repeat the preceding problem for a normalized mean-square error of 0.1 or less. Data From Problem 8.16An SSB system is to be operated with a normalized mean-square error of 0.06 or less. By making a plot of output SNR versus demodulation phase-error variance for the case in which normalized mean-square error is 0.4%, show the region of satisfactory system performance. Repeat for a DSB system. Plot
Answer Preview: This problem is identical to the pr…

, For each case given below, tell whether the given function can be a satisfactory auto correlation function. If it is not satisfactory, give the reason(s).(a) Ra (?) = II (?/?0) where ?0 is a constant;(b) Rb (?) = A (? /?0) where ?0 is a constant;(c) Rc (?) = A cos (2?f0?) where A and f0 are constants;(d) Rd (?) = A + B cos (2?f0?) where A, B, and f0 are constants;(e) Re (?) = A sin (2?f0?) where A
Answer Preview: ( a ) The given function can be a satisfactory auto co…

, Chapter: 2 -Problem: 3 >> The sum of two or more sinusoids may or may not be periodic depending on the relationship of their separate frequencies. For the sum of two sinusoids, let the frequencies of the individual terms be f1 and f2, respectively. For the sum to be periodic, f1 and f2 must be commensurable; i.e., there must be a number f0 contained in each an integral number of times. Thus, if f0 is the largest such numbe
Answer Preview: a Not periodic because f 1 1 Hz and f 2 3 Hz are not commensurable b Periodic T…

, What is an efficient estimate?
Answer Preview: An efficient estimate means the "best possible" or the "optimal" estimation of the parameter of …

, Chapter: 4 -Problem: 12 >> Repeat the preceding problem assuming that m(t) is the triangular pulse 4Λ[1/3(t - 6)]. Data From Problem 11An FM modulator has output where fd = 20 Hz/V. Assume that m(t) is the rectangular pulse m(t) = 4II [1/8(t - 4)](a) Sketch the phase deviation in radians. (b) Sketch the frequency deviation in hertz. (c) Determine the peak frequency deviation in hertz. (d) Determine the peak phase deviation
Answer Preview: a The phase deviation is b The frequency deviation in Hz is c The peak frequency de…

, An FM system operates with the same parameters as given in the preceding drill problem except that the deviation ratio is 5. Determine the channel noise PSD that results in a post detection SNR of 30 dB.
Answer Preview: Noise can be defined as any unwanted signals, random or deterministic, which interfere with the fait…

, Chapter: 3 -Problem: 6 >> Using a sum of sinusoids as the sampling frequency, sample and generate a PAM signal. Experiment with various values of ?fs. Show that the message signal is recovered by low pass filtering. A third-order Butter worth filter is suggested.
Answer Preview: The MATLAB code follows File ce3 6 m clear all t 0 0 001 2 0 001 m zeros 1 2000 x zeros 1 2000 m cos …

, Consider a (5,4) code. What kind of code is this? How many errors per code word can be corrected? How many errors per code word can be detected? Give the generator matrix of this code.
Answer Preview: Any error-correcting code can be used for error detection. A code with minimum …

, Chapter: 3 -Problem: 1 >> In Example 3.1 we determined the minimum value of m(t) using MATLAB. Write a MATLAB program that provides a complete solution for Example 3.1. Use the FFT for finding the amplitude and phase spectra of the transmitted signal xc (t).
Answer Preview: The MATLAB program is File ce3 1 m t 0 0 001 1 fm 1 fc 10 m 4 cos 2 pi fm t pi 9 2 si…

, Chapter: 8 -Problem: 4 >> Derive the equation for yD(t) for an SSB system assuming that the noise is expanded about the frequency fx = fc ±1/2W. Derive the detection gain and (SNR)D. Determine and plot Snc (f) and Sns (f).
Answer Preview: We express n t as where we use the plus sign for the …

, A true rms voltmeter (assumed noiseless) with an effective noise bandwidth of 30 MHz is used to measure the noise voltage produced by the following devices. Calculate the meter reading in each case. (a) A 10 k ? resistor at room temperature, T0 = 290o K.(b) A 10 k ? resistor at 29? K.(c) A 10 k ? resistor at 2.9? K. (d) What happens to all of the above results if the bandwidth is decreased by a fa
Answer Preview: A True RMS Voltmeter Problem According to Nyquist Theorem, Mean Square noise voltage appearing acr…

, Chapter: 4 -Problem: 8 >> Determine and sketch the spectrum (amplitude and phase) of an angle-modulated signal assuming that the instantaneous phase deviation is ?(t) = ? sin(2?fmt). Also assume ? = 10, fm = 30 Hz, and fc = 2000 Hz.
Answer Preview: The amplitude and phase spectra follow directly from …

, Chapter: 2 -Problem: 72 >> Show that x(t) and x? (t) are orthogonal for the following signals: (a) x1(t) = sin (?0t)(b) x2(t) = 2cos (?0t) + sin (?0t) cos (2 ?0t)(c) x3(t) = A exp (j?0t)
Answer Preview: a x a t cos 0 t 2 sin 0 t so b Use trigonometric identities to e…

, Chapter: 9 -Problem: 2 >> Consider an antipodal base band digital transmission system with a noise level of N0 = 10-3 W/Hz. The signal bandwidth is defined to be that required to pass the main lobe of the signal spectrum. Fill in the following table with the required signal power and bandwidth to achieve the error probability/data rate combinations given.
Answer Preview: The bandwidth should be equal to the data rate to pass the main lobe of the signa…

, List three reasons for using spread spectrum.
Answer Preview: Three Reason for using spread spectrum are 1. To prevent interference I e …

, Chapter: 2 -Problem: 64 >> Verify the pulse width-bandwidth relationship of Equation (2.234) for the following signals. Sketch each signal and its spectrum.(a) x(t) = A exp (-t2 / 2?2) (Gaussian pulse) (b) x(t) = A exp (-? |t|), (Gaussian pulse) ? > 0 (double-sided exponential)
Answer Preview: a The Fourier transform of this signal is X f A…

, A two-path channel consists of a direct path and one delayed path. The delayed path has a delay of 5 microseconds. The channel can be considered flat fading if the phase shift induced by the delayed path is 10 degrees or less. Determine the maximum bandwidth of the channel for which the flat-fading assumption holds.
Answer Preview: The maximum bandwidth of the ch…

, Chapter: 2 -Problem: 2 >> A signal has the double-sided amplitude and phase spectra shown in Figure 2.33. Write a time-domain expression for the signal. Transcribed Image Text: |Phase |Amplitude 4 -4 -2 4 4
Answer Preview: By noting the amplitudes and phases o…

, Chapter: 5 -Problem: 1 >> Given the channel features or objectives below. For each part, tell which line code(s) is (are) the best choice(s).(a) The channel frequency response has a null at f = 0 hertz. (b) The channel has a pass band from 0 to 10 kHz and it is desired to transmit data through it at 10,000 bits/s. (c) At least one zero crossing per bit is desired for synchronization purposes. (d) Built-in redundancy is des
Answer Preview: a Split phase or bip…

, Chapter: 9 -Problem: 3 >> Suppose N0 = 10-6 W/Hz and the base band data bandwidth is given by B = R = 1 / T Hz.For the Required Signal Power A2 and BandwidthR, bps PE = 10-3 PE = 10-4 PE = 10-4 PE = 10-5 PE = 10-61,00010,000100,000following bandwidths, find the required signal powers, A2, to give bit error probability of 10-4 along with the allowed data rates:(a) 5 kHz; (b) 10 kHz; (c) 100 kHz; (d) 1 MHz.
Answer Preview: a For P E desired 10 4 we have z required 8 39 dB 6 91 ratio For R B 5 000 bps we …

, Tell what the abbreviations 1G, 2G, 3G, and 4G mean and the approximate dates of their implementation.
Answer Preview: 1G - First generation of wireless analog telephone and it was introduced …

, Chapter: 4 -Problem: 15 >> An audio signal has a bandwidth of 15 kHz. The maximum value of |m(t)| is 10 V. This signal frequency modulates a carrier. Estimate the peak deviation and the bandwidth of the modulator output, assuming that the deviation constant of the modulator is(a) 20 Hz/V (b) 200 Hz/V (c) 2 kHz/V (d) 20 kHz/V
Answer Preview: The results are given in the following table The d…

, Chapter: 5 -Problem: 14 >> (a) Show by a suitable sketch that the trapezoidal spectrum given below satisfies Nyquist’s pulse shaping criterion:P(f) = 2? (f / 2W) - ?(f / W)(b) Find the pulse-shape function corresponding to this spectrum.
Answer Preview: a Consider P f 2 f 2W f W which is a trapezoid 1 uni…

, Chapter: 2 -Problem: 6 >> Write a computer program to find the time duration of a low pass energy signal that contains a certain specified percentage of its total energy, for example, 95%. In other words, write a program to find  with ET set equal to a specified value, where it is assumed that the signal is zero for t < 0. Transcribed Image Text:
Answer Preview: The program for this exercise is similar …

, The JSR un-expectantly increases in a spread spectrum system by 10 dB. What means can be used to combat this?
Answer Preview: even This is the problem based on relation between intensity and power. Off electromagnetic relation …

, Chapter: 3 -Problem: 3 >> Using the same message signal and value for fm used in the preceding computer exercise, show that carrier reinsertion can be used to demodulate an SSB signal. Illustrate the effect of using a demodulation carrier with insufficient amplitude when using the carrier reinsertion technique.
Answer Preview: In this computer example we investigate the demodulation of SSB using carrier resertion for several …

, Chapter: 2 -Problem: 38 >> (a) Find the Fourier transform of the cosine pulse x(t) = AII (2t / T0) cos (ω0t), where ω0= 2Ï€ / T0Express your answer in terms of a sum of sinc functions. Provide MATLAB plots of x(t) and X(f) [note that X(f) is real].(b) Obtain the Fourier transform of the raised cosine pulse Provide MATLAB plots of y(t) and Y(f) [note that Y(f) is real]. Compare with part (a).(c) Use Equation (2.134) with t
Answer Preview: a By the modulation theorem b Use the superposition and modulation theorems to get c In thi…

, Chapter: 5 -Problem: 11 >> Sketch the following spectra and tell which ones satisfy Nyquist€™s pulse-shape criterion. For those that do, find the appropriate sample interval, T, in terms of W. Find the corresponding pulse-shape function p(t). (Recall that II(f/A) is a unit-high rectangular pulse from - A/2 to A/2, Λ (f/B) is a unit-high triangle from -B to B.) (a) (b) (c) (d) (e)
Answer Preview: Nyquists pulse shaping criterion is a sufficient condition Each of these spectra being built of squa…

, Chapter: 10 -Problem: 12 >> (a) Sketch the signal space with decision regions for 16-ary PSK [see (10.47)].(b) Use the bound (10.50) to write down and plot the symbol error probability versus Eb / N0.(c) On the same axes, compute and plot the bit error probability assuming that Gray encoding is used. Transcribed Image Text: 2?
Answer Preview: a The signal points lie on a circle of radius E s centered at the origin equally spaced at angular …

, Compare QPSK, OQPSK, and MSK in as many ways you can think of.
Answer Preview: Quadrature Phase Shift Keying ( QPSK ) is a form of Phase Shift Keyi…

, Chapter: 2 -Problem: 40 >> (a) Obtain the time-average auto correlation function of x(t) = 3 + 6 cos (20?t) + 3 sin (20?t). (Combine the cosine and sine terms into a single cosine with a phase angle.) (b) Obtain the power spectral density of the signal of part (a). What is its total average power?
Answer Preview: a Write 6 cos 20t 3 sin 20t R cos 20t R cos cos 20t R sin sin 20t Thus R cos 6 co…

, Chapter: 5 -Problem: 16 >> Repeat Problem 5.15 for a five-tap zero-forcing equalizer. Data From Problem 5.15Given the following channel pulse response samples: pc (-3T) = 0.001  pc(-2T) = -0.01   pc(-T) = 0.1          pc(0) = 1.0pc (T) = 0.2         pc(2T) = -0.02     pc(3T) = 0.005 (a) Find the tap coefficients for a three-tap zero forcing equalizer. (b) Find the output samples for mT = -2T, -T, 0,T, and 2T.
Answer Preview: a The sample values p c 4T 0 001 and p c 4T 0 003 should have been given The chan…

, Chapter: 12 -Problem: 40 >> Develop the appropriate analysis to verify the correctness of (12.149).
Answer Preview: The probability of n transmissions is the probabili…

, Chapter: 8 -Problem: 6 >> Develop a computer program to verify the performance curves shown in Figure 8.17. Compare the performance of the non-coherent FSK system to the performance of both coherent FSK and coherent PSK with a modulation index of 1. We will show in the following chapter that the bit-error probability for coherent FSK is and that the bit-error probability for coherent BPSK with a unity modulation index iswh
Answer Preview: The MATLAB program for this computer exercise is a simple modification of the program used for Compu…

, A source has three outputs with probabilities 1/6,1/2, and 1/3. Determine the entropy of the source. Give the source probabilities that yield the maximum entropy for a source with three outputs.
Answer Preview: Entropy of source is given by S=P* log 2 ( P )+P * log 2 ( …

, Chapter: 4 -Problem: 11 >> An FM modulator has output where fd = 20 Hz/V. Assume that m(t) is the rectangular pulse m(t) = 4II [1/8(t - 4)](a) Sketch the phase deviation in radians. (b) Sketch the frequency deviation in hertz. (c) Determine the peak frequency deviation in hertz. (d) Determine the peak phase deviation in radians. (e) Determine the power at the modulator output.
Answer Preview: a The phase deviation is which is for 0 t 8 Thus t 0 t 0 t 160t …

, Chapter: 7 -Problem: 25 >> A second-order Butter worth filter has 3-dB bandwidth of 500 Hz. Determine the unit impulse response of the filter and use it to compute the noise-equivalent bandwidth of the filter. Check your result against the appropriate special case of Example 7.9.
Answer Preview: The transfer function is where A j 3 2 with 3 the 3 dB frequency …

, Chapter: 12 -Problem: 16 >> Calculate the entropy of the fourth-order extension of the source defined in Table 12.1.  Determine LÌ…/n for n = 4, and add this result to those shown in Figure 12.9. Determine the efficiency of the resulting codes for n= 1, 2, 3, and 4. Figure 12.9 Transcribed Image Text: Table 12.1 First-Order So
Answer Preview: For the fourth order extension we have The average word length L 1 9702 which is L 4 1 9702 4 0 …

, A random process is defined by the sample functions Xi. (t) = Ait + Bi, where t is time in seconds, the As are in dependent random variables for each i, which are Gaussian with 0 means and unit variances, and the Bis are independent random variables for each ¡ uniformly distributed in [-0.5,0.5].(a) Sketch several typical sample functions.(b) Is the random process stationary?(c) Is the random proc
Answer Preview: a) See attached image for several typical sample functions. b) …

, Chapter: 2 -Problem: 5 >> Write a computer program to find the bandwidth of a lowpass energy signal that contains a certain specified percentage of its total energy, for example, 95%. In other words, write a program to find  with EW set equal to a specified value, where GX (f) is the energy spectral density of the signal. Transcribed Image Text:
Answer Preview: ce2 5 m Finding the energy ratio in a preset bandwidth R Ziemer W Tranter Principles of Communicatio…

, Chapter: 2 -Problem: 30 >> Use the superposition, scale-change, and time-delay theorems along with the transform pairs II(t) †” sinc(f), sinc(t) †” II(f), ˆ§ (t), †” sinc2(f), and sinc2(t) †” ˆ§ (f)  to find Fourier transforms of the following: (a) (b) x2 (t) = 2 sinc[2(t - 1)](c) (d) (e) x5 (t) = 5 sinc [2(t - 1)] + 5 sinc [2 (t - 1)](f)  Transcri
Answer Preview: a The result is X 1 f 2sinc 2f exp j2f b The resul…

, Chapter: 10 -Problem: 21 >> On the basis of 90% power-containment bandwidth, give the required transmission bandwidth to achieve a bit rate of 50 kbps for (a) BPSK (b) QPSK or OQPSK (c) MSK (d) 16-QAM
Answer Preview: Use Figure 10 16 noting that the abscissa is normalized base band bandwidth …

, Chapter: 3 -Problem: 7 >> In this problem we examine the efficiency of AM for the case in which the message signal does not have symmetrical maximum and minimum values. Two message signals are shown in Figure 3.34. Each is periodic with period T, and τ is chosen such that the DC value of m(t) is zero. Calculate the efficiency for each m(t) for α = 0.7 and α = 1. Figure 3.34
Answer Preview: For the first signal 5 T 0 so That 5T 6 m n t m t …

, Chapter: 8 -Problem: 6 >> Assume that an AM system operates with an index of 0.5 and that the message signal is 10 cos(8?t). Compute the efficiency, the detection gain in dB, and the output SNR in decibels relative to the base band performance PT / N0W. Determine the improvement (in decibels) in the output SNR that results, if the modulation index is increased from 0.5 to 0.8.
Answer Preview: The message signal is m t 10 cos 8t Thus m n t cos 8t so that The efficienc…

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, Chapter: 4 -Problem: 30 >> A Costas PLL operates with a small phase error so that sin ? ? ? ? and cos ? ? 1 Assuming that the low pass filter preceding the VCO is modeled as a/(s + ?), where ? is an arbitrary constant, determine the response to m(t) = u(t - t0).
Answer Preview: Since the phase error is assumed small so that cos t 1 the input from the top branch see Figure 4 26 …

, Chapter: 2 -Problem: 37 >> Given the following signals, suppose that all energy spectral components outside the bandwidth |f| ? W  are removed by an ideal filter, while all energy spectral components within this bandwidth are kept. Find the ratio of energy kept to total energy in each case. (?, ?, and ? are positive constants.)(a) x1 (t) = e -?tu(t) (b) x2 (t) = II (t/?) (requires numerical integration)(c) x3 (t) = e-?tu(t)
Answer Preview: a From before the total energy is E 1 total 1 2 The Fourier transform of the given sign…

, Chapter: 10 -Problem: 25 >> Derive the Fourier transform pair given by (10.120). To show:
Answer Preview: To show Use the modulation theorem tog…

, Chapter: 9 -Problem: 3 >> Write a computer program to evaluate the degradation imposed by Gaussian phase jitter at a desired error probability as discussed in connection with the data presented in Table 9.2. This will require numerical integration. Transcribed Image Text: Table 9.2 Effect of Gaussian Phase Reference Jitter
Answer Preview: ce9 3 m Evaluates eect of Gaussian phase error in BPSK fixed variance Uses subprogram pb phase pdf c…

, (a) What is the probability of getting two or fewer heads in tossing a fair coin 10 times? (b) What is the probability of getting exactly five heads in tossing a fair coin 10 times?
Answer Preview: a) Probability of getting a head when a single coin is tossed : p=1/2 Pr…

, Chapter: 4 -Problem: 2 >> Repeat the preceding problem for kp-1/2Ï? and 3/8Ï?. Data From problem 1 Let the input to a phase modulator be m(t) = u(t - t0), as shown in Figure 4.1(a). Assume that the unmodulated carrier is Ac cos(2Ï?fct) and that fct0 = n, where n is an integer. Sketch accurately the phase modulator output for kp = Ï? and -3/8Ï? was done in Figure 4.1(c) for Kp = 1/2Ï?. Figure 4.1(a) Figure 4.1 (c)
Answer Preview: Once again by definition x c t A c cos c t k …

, Chapter: 9 -Problem: 34 >> Consider a base band antipodal PAM system with channel bandwidth of 5 kHz and a desired data rate of 20 kbps. (a) What is the required value for M?(b) What value of Ed / N0 in dB will give a bit error probability of 10-6?0-5?
Answer Preview: a Apply 9 142 since base band is specified …

, Which of the following pulse spectra have inverse Fourier transforms with the zero-ISI property? (a) P1 (f) = II (Tf) where T is the pulse duration;(b) P2 (f) = ? (Tf / 2);(c) P3 (f) = II(2T);(d) P4 (f) = II(Tf) + II (2Tf).
Answer Preview: (a) is correct. (b) is incorrect. For P2 (f), even if the pulse is centered at zero frequency, the …

, Chapter: 3 -Problem: 16 >> Redraw Figure 3.10 to illustrate the generation of upper-side band SSB. Give the equation defining the upper side band filter. Complete the analysis by deriving the expression for the output of an upper-side band SSB modulator. Figure 3.10 Transcribed Image Text: HL f) .f fe fe DSB spectrum ? .f fe
Answer Preview: Consider the filter transfer function shown below From …

, A signal in a simple system is defined by 5 cos [2?(6)t]. This signal is subjected to additive single tone interference defined by 0.2 sin [2?(8)t]. Determine the signal-to-interference ratio. Validate your result, using the techniques illustrated in Section 8.1.5, by calculating Px, Py, Rxy, and the maximum value of Rxy.
Answer Preview: The figure shows the slip-line field for a rigid plasticdouble-not…

, Chapter: 4 -Problem: 14 >> An FM modulator has fc = 2000 Hz and fd = 20 Hz/V. The modulator has input m(t) = 5 cos[2?(10)t].(a) What is the modulation index? (b) Sketch, approximately to scale, the magnitude spectrum of the modulator output. Show all frequencies of interest.(c) Is this narrow band FM? Why?(d) If the same m(t) is used for a phase modulator, what must kP be to yield the index given in (a)?
Answer Preview: a The peak deviation is 20 5 100 and f m 10 Thus the modulation index is 100 10 10 b The magnitude …

, Chapter: 10 -Problem: 41 >> Given the following parameter values from the IEEE802.16 standard:Modulation                         Coding rateBPSK···································1/2BPSK···································3/4QPSK···································1/2QPSK···································3/416-.QAM·······························1/216-QAM································3/464-QAM································
Answer Preview: The equation for the effective rate is Fo…

, Consider a signal-plus-noise process of the form z(t) = A cos 2?(f0 + fd)t + n(t)? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ??(D.29) where n(t) is given by n(t) = nc(t) cos 2?f0t ? ns(t) sin 2?f0t? ? ? ? ? ? ? ? ? ? ? ? ?(D.30) Assume that n(t) is an ideal band limited white-noise process with double-sided power spectral density equal to 1/2 N0, for -1/2 B ? f ? f0 ? 1/2 B, and zero otherwise. Write z(t
Answer Preview: (a) The expression for n_c(t) and n_s(t) c…

, Chapter: 3 -Problem: 28 >> Repeat the preceding problem assuming that the commutator is run at twice the minimum rate. What are the advantages and disadvantages of doing this? Repeat the preceding problemFive messages band limited to W, W, 2W, 4W, and 4W Hz, are to be time-division multiplexed. Devise a commutator configuration such that each signal is periodically sampled at its own minimum rate and the samples are properl
Answer Preview: If the speed of the commutator is doubled from 2W to 4W the sa…

, Tell which binary data format(s) shown in Figure 5.2 satisfy the following properties, assuming random (fair coin toss) data: Figure 5.2 (a)?Zero DC level;(b)?A zero crossing for each data bit;(c) Binary 0 data bits represented by 0 voltage level for transmission and the waveform has nonzero DC level;(d) Binary 0 data bits represented by 0 voltage level for transmission and the waveform has zero
Answer Preview: Answer a Manchester Encoding and Differential Manche…

, An antenna with a temperature of 300° K is fed into a receiver with a total gain of 80 dB, Te = 1500° K, and a bandwidth of 3 MHz.(a) Find the available noise power at the output of the receiver.(b) Find the necessary signal power P in dBm at the antenna terminals such that the output signal-to-noise ratio is 50 dB.
Answer Preview: Given antenna temperature is 300k So T = 300 k, power gain = 80 dB T = 1500 k, Bw = 3mHz …

, Chapter: 3 -Problem: 24 >> A continuous-time signal is sampled and input to a holding circuit. The product of the holding time and the sampling frequency is ? fs. Plot the amplitude response of the required equalizer as a function of ? fs. What problem, or problems, arise if a large value of ? is used while the sampling frequency is held constant?
Answer Preview: From 3 96 the transfer function of the holding operatio…

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, (a) Rank the following binary modulation schemes in terms of Eb / N0 required to give PE = 10-6 from best to worst (the lowest required Eb / N0 is the best system): PSK; coherent FSK; DPSK; coherent ASK; and non coherent FSK.(b) Do the same with respect to bandwidth efficiency.
Answer Preview: (a) PSK > coherent FSK > …

, Chapter: 2 -Problem: 7 >> Which of the following signals are periodic and which are aperiodic? Find the periods of those that are periodic. Sketch all signals.(a) xa (t) = cos (5Ï€t) + sin (7Ï€t) (b) (c)(d) xd (t) = sin(3t) + cos (2Ï€t)(e) (f)  Transcribed Image Text: X, (t) = E, A(t – 2n) 00 %3D n=0 |x, () ?-_ ?-2n) 00 In=
Answer Preview: a c and e are periodic Their periods are 2 s fundamental f…

, Given that Q (?2z) = 10-6  for z = 11.31 find the following:(a) The signal amplitude (assume rectangular pulses) for antipodal base band signaling that gives PE = 10-6 in a channel with N0 = 10-7 W/Hz and a data rate of 1 kbps.(b) Same question as in (a), but for a data rate of 10 kbps.(e) Same question as in (a), but for a data rate of 100 kbps.(d) The signal amplitude for antipodal baseband sign
Answer Preview: ( a ) The signal amplitude for antip od al base band signaling that gives PE = 10 - 6 in a channe…

, Chapter: 2 -Problem: 5 >> (a) Show that the function δε(t) sketched in Figure 2.4(b) has unity area. Figure 2.4 (b) (b) Show thatδε(t) = e-1e-t/εu(t) has unity area. Sketch this function for E = 1,1/2, and 1/4. Comment on its suitability as an approximation for the unit impulse function.(c) Show that a suitable approximation for the unit impulse function as ε †’ 0 is given by otherwise.
Answer Preview: a This function has area where a tabulated integral has been …

, Chapter: 2 -Problem: 51 >> Using the Paley-Wiener criterion, show that|H(f)| = exp (-?f2)is not a suitable amplitude response for a causal, linear time-invariant filter.
Answer Preview: Application of the Payley Wiener criter…

, What is a major use of OFDM? What advantages does it provide?
Answer Preview: OFDM stands for Orthogonal Frequency Division Multiplexing. Major use: In wideband digital communi…

, Chapter: 4 -Problem: 3 >> Redraw Figure 4.4 assuming m(t) = A sin (2πfmt + π/6) Figure 4.4 Transcribed Image Text: R(t) fm fm fm ?() R(t) Re Re Ac Ac fm (a) if fc +fm fe - fm fc fe-fm fe fe+ fm (b) fe +fm .f fe-fm fe fe-fm fe fe+ fm -f (c) Phase Amplitude Phase Amplitude
Answer Preview: With Figure 4 1 Figure 4 2 we have for AM where is the modu…

, Chapter: 8 -Problem: 10 >> A square-law demodulate for AM is illustrated in Figure 8.20. Assuming that xc(t) = Ac[1 + amn (t)] cos(2Ï€fct) and m(t) = cos(2Ï€fmt) + cos(4Ï€fmt), sketch the spectrum of each term that appears in yD(t). Do not neglect the noise that is assumed to be band limited white noise with bandwidth 2W. In the spectral plot, identify the desired component, the signal-induced distortion, and the noise. Fig
Answer Preview: Let the predetection filter band width be B T and let the post detection filter bandwidth be B D The …

, Explain the principle of using a sufficient statistic in making a decision or estimating a parameter.
Answer Preview: If "no other statistic that can be obtained f…

, Chapter: 2 -Problem: 3 >> Write a computer program to evaluate the coefficients of the complex exponential Fourier series of a signal by using the fast Fourier transform (FFT). Check it by evaluating the Fourier series coefficients of a square wave and comparing your results with Computer Exercise 2.2.
Answer Preview: ce2 3 m FFT plotting of line spectra for half rectified full rectified sinewave square wave and triangular waveforms R Ziemer W Tranter Principles of …

, Chapter: 8 -Problem: 9 >> An envelope detector operates above threshold. The modulating signal is a sinusoid. Plot (SNR)D in decibels as a function of PT/N0W for the modulation index equal to 0.3, 0.5, 0.6, and 0.8.
Answer Preview: Since m t is a sinusoid m 2 n 1 2 and the efficiency is and the outpu…

, A band pass random process has power spectral density S(f) = II (f - 10/4) + II (f + 10/4).(a) Find its auto correlation function. (b) It is to be represented in in phase quadrature form; that is, x(t) = nc (t) cos (2?f0t + ?) - ns (t) sin (2?f0t + ?). If f0 is chosen as 10 Hz, what is the cross-spectral density, Sncns (f)?(c) If f0 is chosen as 8 Hz, what is the cross-spectral density, Sncns (f)?
Answer Preview: a) The auto correlation function for this band pass random process is given by: Rxx() = S(f)e^(-2ift…

, Chapter: 3 -Problem: 6 >> A message signal is a square wave with maximum and minimum values of 8 and -8 V, respectively. The modulation index ? = 0.7 and the carrier amplitude Ac = 100 V. Determine the power in the side bands and the efficiency. Sketch the modulation trapezoid.
Answer Preview: Using 3 14 with A c 100 0 7 and m 2 n t 1 gives x 2 c t 0 5 100 2 0 5 1…

, Chapter: 8 -Problem: 7 >> An AM system has a message signal that has a zero mean Gaussian amplitude distribution. The peak value of m(t) is taken as that value that |m(t)| exceeds 1.0% of the time. If the index is 0.8, what is the detection gain?
Answer Preview: The first step is to determine the value of M …

, A filter has frequency response function H (f) = ?(f / 2). What is its noise- equivalent bandwidth?
Answer Preview: Equivalent noise bandwidth is the bandwidth of a perfect rectangular …

, Chapter: 4 -Problem: 31 >> In this problem we wish to develop a base band (low pass equivalent model) for a Costas PLL. We assume that the loop input is the complex envelope signal x?(t) = Ac m(t) ej?(t)and that the VCO output is ej?(t). Derive and sketch the model giving the signals at each point in the model.
Answer Preview: With the assumed VCO output represented by e j t we have t…

, Chapter: 2 -Problem: 60 >> The nonlinear system defined by y(t) = x(t) + 0.1x2 (t) has an input signal with the band pass spectrum Sketch the spectrum of the output, labeling all important frequencies and amplitudes. Transcribed Image Text: f + 10 + 211 f – 10 X(f)= 21 4
Answer Preview: In terms of the input spectrum the output spectrum is Where …

, Chapter: 8 -Problem: 8 >> Assume a three-bit ADC (eight quantizing levels). We desire to design a compounding system consisting of both a compressor and ex-pander. Assuming that the input signal is a sinusoid, design the compressor such that the sinusoid falls into each quantizing level with equal probability. Implement the compressor using a MATLAB program, and verify the compressor design. Complete the com-pander by desi
Answer Preview: Since the signal is a sinusoid we can use an inverse sin function as a compressor characterist…

, Consider the circuit shown in Figure A.8. (a) Obtain an expression for the mean-square noise voltage appearing across R3. (b) If R1 = 2000 ?, R2 = RL = 300 ?, and R3 = 500 ?, find the mean-square noise voltage per hertz. Transcribed Image Text: R2 RL R3 R1
Answer Preview: a. Circuit for noise calculations b. R = 2000 Voz (a) Resistor Network R = 300 wwww …

, Given a junction diode with reverse saturation current Is = 15 ?A.(a) At room temperature (290?K), find V such that I > 20Is, thus allowing (A.16) to be approximated by (A.17). Find the rms noise current.(b) Repeat part (a) for T =290?K.
Answer Preview: (a) For voltage V = 15 A in the …

, Chapter: 6 -Problem: 22 >> Ifshow that (a) E[X2n] = 1 · 3 · 5 ··· (2n - 1) σ2n, for n = 1,2,...(b) E[X2n-1] = 0 for n = 1,2,... Transcribed Image Text: fx(x) -(2? ?') exp 2?2
Answer Preview: a The integral evaluates as follows where y x 2 1 2 …

, A source with equivalent noise temperature Ts = 1000? K is followed by a cascade of three amplifiers having the specifications shown in Table A. 1. Assume a band width of 50 kHz. (a) Find the noise figure of the cascade. (b) Suppose amplifiers 1 and 2 are interchanged. Find the noise figure of the cascade. (c)?Find the noise temperature of the systems of parts (a) and (b). (d)?Assuming the configu
Answer Preview: ( a ) The noise figure of the cascade is 7 . 25 dB . ( b ) The noise figure of the cascade is 6 . 23 dB . ( c ) The noise temperature of the system in …

, Chapter: 3 -Problem: 9 >> Rework Problem 3.8 for the message signal m(t) = 9 cos(20?t) + 8 cos(60?t)Data from Problem 3.8(a) Write the equation for mn(t), the normalized signal with a minimum value of -1.(b) Determine {m2n(t)}, the power in mn(t).(c) Determine the efficiency of the modulator.(d) Sketch the double-sided spectrum of xc(t), the modulator output, giving the weights and frequencies of all components.
Answer Preview: a With m t 9 cos 20t 8 cos 60t the most negative value of m t 17 and …

, Chapter: 6 -Problem: 24 >> Two random variables X and Y have means and variances given below:mx = 1 ?2x = 4 my = 3 ?2y = 7 A new random variable Z is defined as Z = 3X - 4Y Determine the mean and variance of Z for each of the following cases of correlation between the random variables X = Y:(a) PXY = 0(b) PXY = 0.2(c) PXY = 0.7(d) PXY = 1.0
Answer Preview: Regardless of the correlation coefficient the mean of Z …

, A binary symmetric channel has an error probability of 0.001. Determine the channel capacity.
Answer Preview: For Binary Symmetric Channel: Error Probability (P) = 0 001 (Given) Channel Capacit…

, Chapter: 3 -Problem: 18 >> Prove analytically that carrier reinsertion with envelope detection can be used for demodulation of VSB.
Answer Preview: We assume that the VSB waveform is given by We let y t be x c t …

, Chapter: 5 -Problem: 17 >> A simple model for a multi path communications channel is shown in Figure 5.20(a). Figure 5.20 (a) (a) Find Hc (f) = Y(f) / X (f) for this channel and plot |Hc(f)| for β = 1 and 0.5.(b) In order to equalize, or undo, the channel-induced distortion, an equalization filter is used. Ideally, its frequency response function should be Heq (f) = 1 / Hc(f)if the effects of noise are ignored and only dis
Answer Preview: a The output in terms of the input is y t x t x t m Using the superposition and time delay …

, Choose the correct adjective: A narrower bandwidth channel implies (more) (less) amplitude jitter.
Answer Preview: A narrow bandwidth channel implies …

, Chapter: 3 -Problem: 29 >> Five messages band limited to W, W, 2W, 5W and 7W, Hz, respectively, are to be time-division multiplexed. Devise a sampling scheme requiring the minimum sampling frequency.
Answer Preview: The minimum base band bandwidth is B W W 2W 5W 7W 16W A suitable scheme for this takes a bit …

, Chapter: 5 -Problem: 13 >> It is desired to transmit data at 9 kbps over a channel of bandwidth 7 kHz using raised-cosine pulses. What is the maximum value of the roll-off factor, ?, that can be used?
Answer Preview: Use 5 37 and set the m…

, Chapter: 10 -Problem: 32 >> For a PN sequence of length 27 - 1 = 127 two possible feedback connections are x4 ? x7 and x6 ? x7.(a) Draw a block diagram of the feedback shift register for the connection x4 ? x7.(b) Compute the PN sequence corresponding to the connection x4 ? x7.(c) Draw a block diagram of the feedback shift register for the connection x6 ? x7.(d) Compute the PN sequence corresponding to the connection x6 ? x7
Answer Preview: a The two boxes with arrows below are modulo 2 summed and the sum fed bac…

, A (7,4) single error-correcting code has the source symbols in positions 1, 2, 6, and 7. Write the generator matrix for this code.
Answer Preview: Parity Coding: Add one more bit which is the sum of all the message. Ex for '11001001', we will se…

, Chapter: 2 -Problem: 74 >> Following Example 2.30, considerx(t) = 2 cos (52?t)Find x? (t), xp (t), x? (t), xR (t), and xI (t) for the following cases: (a) f0 = 25 Hz; (b) f0 = 27 Hz; (c) f0 = 10 Hz; (d) f0 = 15 Hz; (e) f0 = 30 Hz; (f) f0 = 20 Hz.
Answer Preview: The Hilbert transform of the given signal is x t 2 sin 52t The signal …

, Chapter: 6 -Problem: 15 >> (a) For what value of ? > 0 is the function f(x) = ?x-2u(x - ?)a probability-density function? Use a sketch to illustrate your reasoning and recall that a pdf has to integrate to one. [u(x) is the unit step function.] (b) Find the corresponding cumulative-distribution function. (c) Compute P(X ? 10).
Answer Preview: a Use normalization of the pdf …

, Chapter: 12 -Problem: 39 >> Repeat the preceding problem assuming a (23,12) Golay code. Data From Problem 12.38A source produces binary symbols at a rate of 5000 symbols per second. The channel is subjected to error bursts lasting 0.2 s Devise an encoding scheme using an interleaved (n,k) Hamming code, which allows full correction of the error burst. Assume that the information rate out of the coder is equal to the informati
Answer Preview: The source rate is r s 5000 symbols second The channel symbol rate is …

, Name the three things that must be known in order to design a Bayes receiver.
Answer Preview: 1) Input/ Output Sy…

, Chapter: 2 -Problem: 1 >> Writea computer program to sum the Fourier series for the signals given in Table 2.1. The number of terms in the Fourier sum should be adjustable so that one may study the convergence of each Fourier series. Transcribed Image Text: Table 2.1 Fourier Series for Several Periodic Signals Signal (one pe
Answer Preview: ce2 1 m Amplitude spectra and Fourier series synthesized for various periodic waveforms R Ziemer W T…

, Chapter: 2 -Problem: 49 >> A second-order active band pass filter (BPF), known as a band pass Sallen-Key circuit, is shown in Figure 2.37. (a) Show that the frequency response function of this filter is given by whereω0 = ˆš2(RC) -1Q = ˆš2 / 4 - kK = 1 + Ra / Rb (b) Plot |H (f)|.(c) Show that the 3-dB bandwidth of the filter can be expressed as B = f0 / Q, where f0 = ω0 / 2Ï€.(d) Design a BPF using this circuit with cente
Answer Preview: a Replace the capacitors with 1 jC which is their ac equivalent impedance Call the junction of the i…

, Chapter: 6 -Problem: 36 >> Consider the Cauchy density functionfX(x) = K / 1 + x2 , -? ? x ? ?(a) Find K.(b) Show that var {X} is not finite.(c) Show that the characteristic function of a Cauchy random variable is Mx(jv) = ? Ke-|v|.(d) Now consider Z = X1 + ··· + XN where the Xi ’s are independent Cauchy random variables. Thus, their characteristic function is Mz(jv) = (? K)N exp (-N|v|)Show that fz(z) Cauchy. (fz(z) is not
Answer Preview: a K 1 b E X is not defined but one could argue that it is zero from the oddn…

, Chapter: 10 -Problem: 44 >> (a) Show that the distance from a hexagon cell center to a vertex is 1 / ?3 if adjacent cell centers are 1 unit apart.(b) Show that the distance between cochannel cell centers is Dco = ?N in a hexagonal geometry.
Answer Preview: a Consider a hexigon made up of six equalateral …

, Compare M-ary PSK and QAM in terms of power and bandwidth efficiency.
Answer Preview: M-array PSK : This is the type of digital modulation technique used for data transmission in which i…

, Chapter: 3 -Problem: 5 >> Using MATLAB simulate delta modulation. Generate a signal, using a sum of sinusoids, so that the bandwidth is known. Sample at an appropriate sampling frequency (no slope overload). Show the stair step approximation. Now reduce the sampling frequency so that slope overload occurs. Once again, show the stair step approximation.
Answer Preview: The MATLAB program used appears below Given the annotations the code should be understandable Thanks …

, Chapter: 6 -Problem: 41 >> A random variable X has the probability-density functionExpress the following probabilities in terms of the Q-function and calculate numerical answers for each:(a) P(IXI ‰¤ 15);(b) P(10 < X ‰¤ 20);(c) P(5 < X ‰¤ 25);(d) P(20 < X ‰¤ 30). Transcribed Image Text: e-(x-10)²/50 fx(x) = ? V50?
Answer Preview: The following relationships involving the …

, Chapter: 10 -Problem: 16 >> Show that for M-ary QAMwhere Es is the symbol energy averaged over the constellation of M signals, which is (10.58). The summation formulaswill prove useful. Transcribed Image Text: ??, a 2 (M – 1) ? (?+1) ? (?+1)(2m + 1) ? ? ? and >i = 6. i=1 i=1
Answer Preview: The expression for a follows by computing the average symbol energy in terms of a T…

, (a) A source outputs 73 equally likely messages. Determine the information, in bits, associated with each message. (b) Repeat assuming that there are 37 equally likely messages.
Answer Preview: a) Probability (P) of each source output is 1/7^3 I e 1/343 …

, Chapter: 3 -Problem: 4 >> In this computer exercise we investigate the properties of VSB modulation. Develop a computer program (using MATLAB) to generate and plot a VSB signal and the correspondin

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12 Reviews for Principles of Communications Systems, Modulation and Noise Textbook Questions And Answers