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engineering
telecommunication engineering

Questions and Answers of Telecommunication Engineering

Equation (8.14) is one formulation of the Friis free-space equation. Show that this equation can also be formulated in the following equivalent forms: where Pt is the transmitted power, At is the
From the mathematical definition of the free-space loss we see that it is dependent on the carrier wavelength A or frequency f. How can this dependence on wavelength or frequency be justified in
In a satellite communication system, the carrier frequency used on the uplink is always higher than the carrier frequency used on the downlink. Justify the rationale for this choice.
A continuous-wave (CW) beacon transmitter is located on a satellite in geostationary orbit. The beacon’s 12 GHz output is monitored by an earth station positioned 40,000 km from the satellite. The
Consider a 75-Ω resistor maintained at “room temperature” of 290K. Assuming a bandwidth of 1 MHz, calculate the following;(a) The root-mean-square (RMS) value of the voltage appearing across
In this problem, we revisit Example 8.1 based on the receiver configuration of Figure. Suppose that a lossy waveguide is inserted between the receiving antenna and the low-noise amplifier. The
Consider the receiver of Figure which consists of a ios.sy waveguide, low-noise RF amplifier, frequency down-converter mixer), and IF amplifier. The figure includes the noise figures and power gains
In this problem we address the uplink power budget of the digital satellite communication system considered in Example 8.2. The parameters of the link are as follows: Carrier frequency? ? ? ? ? ? ? ?
The downlink C/N0 ratio in a direct broadcast satellite (DBS) system is estimated to be 85dB-Hz. The specifications of the link are:Satellite ELRP
Both wireless communications and satellite communications rely on radio propagation for their operations. Summarize(a) The similarities of these two multiuser communication systems, and(b) The major
In wireless communication systems, the carrier frequency on the uplink reverse link) smaller than the carrier frequency on the downlink (forward link), justify the rationale for this choice.
Figure depicts the direct (line-of-sight) and indirect (reflected) paths of a radio link operating over a plane earth. The heights of the transmitting antenna at the base station and the receiving
The two-path model defined by the impulse response h(t) = a1 δ(t – τ1) + a2 exp(–jθ) δ(t – τ2) is frequently used in the analytic treatment of wireless communication systems. The model
In the RAKE receiver illustrated in Figure each correlator is synchronized by inserting the right delay into the received signal.(a) Show that, in theory, the same result is obtained by inserting the
Consider the array signal processor of Figure where there are only two users (N = 2) and the array consists of two elements (M = 2). Construct the subspace W for this problem. Hence, using a
In this problem we derive the complex LMS algorithm. Referring to figure and starting with the instantaneous cost function where e[n] is the error signal and M is the number of antenna elements, do
A practical limitation of an adaptive antenna array using the LMS algorithm is the dynamic range over which the array can operate. This limitation is due to the fact that the speed of response of the
In this problem we derive the direct matrix inversion algorithm for adjusting the weights of an adaptive antenna array. To do so, we revisit the derivation of the Wiener filter presented. (a) Show
Let p denote the probability of some event. Plot the amount of information gained by the occurrence of this for 0 < p < 1.
A source emits one of four possible symbols during each signaling interval. The symbols occur with the probabilities: P0 = 0.4, P1 = 0.3, P2 = 0.2, P3 = 0.1 find the amount of information gained by
A source emits one of four symbols s0, s1, s2, and s3 with probabilities 1/3, 1/6, 1/4, and 1/4, respectively. The successive symbols emitted by the source are statistically independent. Calculate
Let X represent the outcome of a single roll of a fair die. What is the entropy of X?
The sample function of a Gaussian process of zero mean and unit variance is uniformly sampled and then applied to a uniform quantizer having the input-output amplitude characteristic shown in Figure.
Consider a discrete memory less source with source alphabet L {s0, s1,. . . , sk–1) and source statistics (p0, p1, ... pk–1,) The nth extension of this source is another discrete memory less
Consider a discrete memory less source with source alphabet L = {s0, s1, s2,) and source statistics [0.7, 0.15, 0.15].(a) Calculate the entropy of the source.(b) Calculate the entropy of the
It may come as a surprise, but the number of bits needed to store text is much less than that required to store its spoken equivalent. Can you explain the reason for it?
Consider a discrete memory less source whose alphabet consists of K equiprobable symbols.(a) Explain why the use of a fixed-length code for the representation of such a source is about as efficient
Consider the four codes listed below:(a) Two of these four codes are prefix codes. Identify them, and construct their individual decision trees.(b) Apply the Kraft—McMillan inequality to codes 1,
Consider a sequence of letters of the English alphabet with their probabilities of occurrence as given here:Letter a
A discrete memory less source has an alphabet of seven symbols whose probabilities of occurrence are as described here:Symbol s0
Consider a discrete memory less source with alphabet (s0, s1, s2,) and statistics {0.7, 0.15, 0.15) for its output.(a) Apply the Huffman algorithm to this source. Hence, show that the average code
Figure shows a Huffman tree. What is the code word for each of the symbols A, B, C, D, E, F, and C represented by this Huffman tree? What are their individual codeword lengths?
A computer executes four instructions that are designated by the code words (00, 01, 10, 11). Assuming that the instructions are used independently with probabilities (1/2, 1/8, 1/8, 1/4), calculate
Consider the following binary sequence it 10 1001100010110 100Use the Lempel—Ziv algorithm to encode this sequence. Assume that the binary symbols 0 and 1 are already in the codebook.
Consider the transition probability diagram of a binary symmetric channel shown in figure. The input binary symbols 0 and 1 occur with equal probability. Find the probabilities of the binary symbols
Repeat the calculation in Problem, assuming that the input binary symbols 0 and 1 occur with probabilities 1/4 and 3/4, respectively.
Consider a binary symmetric channel characterized by the transition probability p. Plot the mutual information of the channel as a function of p1, the a priori probability of symbol 1 at the channel
Figure depicts the variation of the channel capacity of a binary Symmetric channel with the transition probability p. Use the re-suits of problem to explain this variation.
Consider the binary symmetric channel described in Figure. Let Po denote the prob. ability of sending binary symbol x0 = 0, and let p1 = 1 ? P0 denote the probability of sending binary symbol x1 = 1,
Two binary symmetric channels are connected in cascade, as shown in figure. Find the overall channel capacity of the cascaded connection, assuming that both channels have the same transition
The binary erasure channel has two inputs and three outputs as described in figure. The inputs are labeled 0 and 1, and the outputs are labeled 0, 1, and e. A traction a of the incoming bits are
Consider a digital communication system that uses a repetition code for the channel encoding/decoding. In particular, each transmission is repeated times, where n = 2m + 1 is an odd integer. The
Let X1, X2, . . , Xn denote the elements of a Gaussian vector X. The Z are independent with mean ?i and variance ?2i, i = 1, 2,. . . , n. Show that the differential entropy of the vector X equals
A continuous random variable X is constrained to a peak magnitude M that is ? M (a) Show that the differential entropy of X is maximum when it is uniformly distributed, as shown by (b) Show that the
Prove the properties given in Equations 979) to (9.81) for the mutual information I(X; Y).
Consider the continuous random variable Y defined by Y = X + N where X and N are statistically independent. Show that the conditional differential entropy of Y, given X equals h(Y|X) = h(N) where
A voice-grade channel of the telephone network has a bandwidth of 3.4 kHz.(a) Calculate the information capacity of the telephone channel for a signal-to-noise ratio of 30dB.(b) Calculate the minimum
Alphanumeric data are entered into a computer from a remote terminal through a grade telephone channel. The channel has a bandwidth of 3.4 kHz and output signal noise ratio of 20 dB. The terminal has
A black-and-white television picture may be viewed as consisting of approximately 3 x 105 elements, each of which may occupy one of 10 distinct brightness levels with equal probability. Assume that
In this problem, we continue with Example 9.9. Suppose that the tightly packed constellation of Figure b is scaled upward so that the transmitted signal energy per symbol is maintained at the same
The squared magnitude response of a twisted-pair channel can be modeled as |H(f)|2 = exp(-a?f), the constant a is defined by where k is a constant depending on wire gauge, l is a reference line
Equation (9.138) for the signal-to-noise ratio (SNR) of a vector quantizer includes the SNR formula of Equation (3.33) for standard pulse-code modulation as a special case for which k = 1. Justify
All practical data compression and data transmission schemes lie between two limits set by the rate distortion function and the channel capacity theorem. Both of these theorems involve the notion of
In this problem, we revisit Example 9.12, which deals with coded binary antipodal signaling over an additive white Gaussian noise (AWGN) channel. Starting with Equation (9.112) and the underlying
Suppose that nonlinear devices are available for which the output current i o and input voltage v i are related by i o = a1vi + a3 v3i, where a= and a3 are constant. Explain how these
Figure shows the circuit diagram of a square-law modulator. The signal applied to the non linear devices is relatively weak, such that it can be represented by a square law: v2 (t) = a1v1 (t) + a2v21
Figure a show the circuit diagram of a switching modulator. Assume that the carrier wave c (t) applied to the diode is large in amplitude, so that the diode acts like an ideal switch: it presents
Consider the AM signal s (t) = Ac [1 + μ cos (2πƒmt)] cos (2πƒct) produced by a sinusoidal modulating signal of frequency ƒm. Assume that the modulation factor μ = 2, and the carrier frequency
Figure shows the circuit diagram of an envelope detector. It consists simply of a diode and resistor-capacitor (RC) filter. On a positive half-cycle of the input signal, the diode is forward-biased
Consider a square-law detector; using a nonlinear device whose transfer characteristics is defined by v2 (t) = a1v1 (t) + a2v21 (t), where a1 and a2 are constant, v1 (t) is the input, and v2 (t) is
The AM signal s (t) = Ac [1 + ka m (t)] cos (2??ct) is applied to the system in Figure. Assuming that | ka m (t) | ? W and that the carrier frequency ?c > 2W show that m (t) can be obtained from
Consider a message signal m (t) with the spectrum shown in Figure. The message bandwidth W = 1 kHz. This signal is applied to a product modulator, together with a carrier wave Ac cos (2??ct),
Figure shown the circuit diagram of a balanced modulator, the input applied to the top AM modulator is m (t), where as that applied to the lower AM modulator is – m (t); these two modulators have
A DSB-SC modulated signal is demodulated by applying it to a coherent detector.(a) Evaluate the effect of a frequency error Δƒ in the local carrier frequency of the detector, measured with respect
Consider the DSB-SC signal s (t) = Ac cos (2πƒct) m (t), where Ac cos (2πƒct) is the carrier wave and m (t) is the message signal. This modulated signal is applied to a square-law device
Consider the quadrature-carrier multiplex system of Figure. The multiplexed signal s (t) produced at the transmitter output in Figure a is applied to a communication channel of frequency response H
Suppose that in the receiver of the quadrature-carrier multiplex system of Figure b, the local carrier available for demodulation has a phase error Φ with respect to the carrier source used in the
A particular version of AM stereo uses quadrature multiplexing. Specifica.lly, the carrier Ac cos (2πƒct) is used to modulate the sum signal m= (t) = V0 + ml (t) + mr (t), where V0 is a DC offset
Using the message signal m (t) = 1/1 + t2, determine and sketch the modulated waves for the following methods of modulation:(a) Amplitude modulation with 50 percent modulation.(b) Double
The Hilbert transform of a Fourier transformable signal m (t), denoted by m (t), is defined by below, in the frequency domain, we have M (?) = -j sgn (?) M (?), where m (t) ? M (?), m (t) ? M (?),
The local oscillator used for the demodulation of an SSB signal s (t) has a frequency error Δƒ measured with respect to the carrier frequency ƒc used to generate s (t). Otherwise, there is perfect
Figure shows the block diagram of Weaver?s method for generating SSB modulated waves. The message (modulating) signal m (t) is limited to the band ?a | ? | ?b. The auxiliary carrier applied to the
The spectrum of a voice signal m (t) is zero outside the interval ƒa < | ƒ | < ƒb. To ensure communication privacy, this signal is applied to a scramble that consists of the following
In this problem we derive Equation that defines the frequency response HQ (?) of the filter that operates on the message signal m (t) to produce m` (t) for VSB modulation. The signal m` (t), except
The single-tone modulating signal m (t) = Am cos (2πƒmt), is used to generate the VSB signal, where a is a constant, less than unity, representing the attenuation of the upper side frequency.(a)
In this program we study the idea of mixing in a super heterodyne receiver. To be specific, consider the block diagram of the mixer shown in Figure that consists of a product modulator with a local
Figure shows the block diagram of a beterodyne spectrum analyzer. It consists of a variable-frequency oscillator, multiplier, band-pass filter, and root mean square (RMS) meter. The oscillator has
Sketch the PM and FM waves produced by the saw tooth wave shown inFigure.
In frequency-modulated radar, the instantaneous frequency of the transmitted carrier is varied as in Figure, which is obtained by using a triangular modulating signal. The instantaneous frequency of
The instantaneous frequency of a sine wave is equal to ƒc –Δƒ for | t | < T/2, and ƒc for | t | < T/2. Determine the spectrum of this frequency-modulated wave.
Single-sideband modulation may be viewed as a hybrid form of amplitude modulation and frequency modulation. Evaluate the envelope and instantaneous frequency of an SSB wave for the following two
Consider a narrow b and FM signal approximately defined by s (t) = Ac cos (2??ct) ? ?Ac sin (2??ct) sin (2??mt) (a) Determine the envelope of this modulated signal. What is the ratio of the maximum
The sinusoidal modulating wave m (t) = Am cos (2πƒmt) is applied to a phase modulator with phase sensitivity kp. The unmodulated carrier wave has frequency ƒc and amplitude Ac.(a) Determine the
Suppose that the phase-modulated signal of Problem has an arbitrary value for the maximum phase deviation βp. This modulated signal is applied to an ideal band-pass filter with mid-band frequency
A carrier wave is frequency-modulated using a sinusoidal signal of frequency ƒm and amplitude Am.(a) Determine the values of the modulation index β for which the carrier component of the FM signal
An FM signal with modulation index β = 1 is transmitted an ideal band-pass filter with mid-band frequency ƒc and bandwidth 5ƒm, where ƒc is the carrier frequency and ƒm is the frequency of the
A carrier wave of frequency 100 MHz is frequency-modulated by a sinusoidal wave of amplitude 20 volts and frequency 100 kHz. The frequency sensitivity of the modulator is 2.3 kHz per volt.(a)
Consider a wideband PM signal produced by a sinusoidal modulating wave Am cos (2πƒmt), using a modulator with a phase sensitivity equal to k p radius per volt.(a) Show that if the maximum phase
Figure shows the block diagram of a real-time spectrum analyzer working on the principle of frequency modulation. The given signal g (t) and a frequency-modulated signal s (t) are applied to a
An Fm signal with a frequency deviation of 10 kHz at a modulation frequency of 5 kHz is applied to two frequency multiplier connected is cascade. The first multiplier doubles the frequency and the
Figure shows the block diagram of a wideband frequency modulator using the indirect method. This modulator is used to transmit audio signals containing frequencies in the range of 100 Hz to 15 kHz by
Figure shows the frequency-determining network of a voltage-controlled oscillator. Frequency modulation is provided is produced by applying the modulating signal Am sin (2??mt) plus a bias Vb to a
The Fm signal is applied to the system shown in Figure consisting of a high-pass RC filter and an envelope detector. Assume that (a) The resistance R is small compared with the reactance of the
Consider the frequency demodulation scheme in Figure in which the incoming FM signal s (t) is passed through a delay line that produces a phase-shift of ?/2 radians at the carrier frequency ?c. The
Figure shows the block diagram of a zero-crossing detector for demodulating an FM signal, its consist of a limiter, a pulse generator for producing a short pulse at each zero-crossing of the input,
Suppose that the received signal is an FM system contains some residual amplitude modulation of positive amplitude a (t), as shown by s (t) = a (t) cos [2??ct + ? (t)], where ?c is the carrier
(a) Let the modulated wave s (t) in Problem 2.42 be applied to a hard limiter, whose output z (t) is defined by below, show that the limiter output may be expressed in the form of a Fourier series as
(a) Consider an FM signal if carrier frequency ƒc, which is produced by a modulating signal m (t). Assume that ƒc is large enough to justify treating this FM signal as a narrowband signal. Find an
The single sideband version of angle modulation is defined by s (t) = exp [-Φ (t)] cos (2πƒct + Φ (t)], where Φ (t) is the Hilbert transform of the phase function Φ (t), and ƒc is the carrier
Evaluate the autocorrelation functions and cross-correlation functions of the in-phase and quadrature components of the narrowband noise at the coherent detector input for(a) The DSB-SC system,(b) An

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