EEEN3005J: Communication Theory SEMESTER II FINAL EXAMINATION - 2018/2019

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EEEN3005J: Communication Theory

SEMESTER II FINAL EXAMINATION - 2018/2019

Question 1:

A baseband signal, g (t) , with bandwidth 10 kHz, is such that its amplitude satisfies jg (t)j < 0.8 V, and has average power = 0.1 Watts. This signal is connected to a circuit composed of a mixer and an adder as shown in Figure 1 below. The resulting signal, ˜(s)(t) , is transmitted through a channel as shown. The scaling factor, α , represents a signal power attenuation of 120 dB, and w (t) is additive white Gaussian noise with single-sided power spectral density (PSD) N0 = -174 dBm/Hz. The receiver applies an ideal band pass filter having bandwidth just su伍cient to capture the whole of the received modulated signal.

[Note that if the power of a signal is Pm  mWatts, then its power in dBm is = 10 log10(Pm ) dBm.] 

Figure 1: Circuit to be considered in question 1

1. Sketch the time-domain signal, ˜(s)(t), showing numbers and units on both axes.  What name is given to this type of modulation?

2. Calculate the signal-to-noise ratio (SNR) in dB at point “A” . Do not count the carrier component as contributing to the “signal power” here, as it bears no information.

3. What do we mean when we say that a random signal is wide-sense  stationary?

4. What is meant by the Energy  Spectral  Density  (ESD) of a deterministic energy sig- nal?Consider a signal,x (t), with one-sided ESD given by:

Determine the fraction of the signal’s energy that lies in the frequency range 0  < f <  5 kHz

Question 2:

Consider the circuit in Figure 2 where the control signal c (t), that is guaranteed to be either ±1 V, is used to control the position of the two switches as shown. 

Figure 2: Circuit to be considered in question 2

1. Write a simple expression for the circuit’s output, vout (t), in terms of c (t) and ˜(s)(t), explaining your answer by clearly describing the operation of the circuit when c (t) = +1 V and when c (t) = -1 V.

2. Let ˜(s)(t) be a bandpass signal with centre frequency fc  Hz, and c (t) be a square wave signal alternating between ±1 V also with frequency fc  Hz. In this case

•  sketch a possible power spectral density (PSD) for ˜s(t)

•  sketch the PSD of c (t)

•  sketch the resulting PSD of vout (t)

3. Provide a clear definition of \Double SideBand Suppressed Carrier (DSB-SC)" modu- lation. Your answer should contain the mathematical expressions and derivations of a DSB-SC signal in the time and frequency domain. You should also include sketches of an example DSB-SC signal in both domains.

4. Explain how the circuit in Figure 2 could be used, in conjunction with some additional circuit elements, to demodulate a DSB-SC signal.

5. The process of demodulating a DSB-SC signal often sufers from local oscillator \phase and/or frequency mismatch" errors. Explain the meaning of this statement

Question 3:

1. What is the instantaneous frequency fi  (t) of an arbitrary signal A (t) cos (φ (t))?

2. If a modulated signal can be written as Ac cos (2πfct + θ (t)) give an expression for the instantaneous frequency.

3. What is Frequency Modulation (FM)? your answer should derive an expression for ˜s(t), the FM signal, in terms of g (t) the modulating signal, and kf  the frequency sensitivity.

4. Let g (t) be a sine wave with amplitude Am  and frequency fm  kHz.

• Derive an expression for ˜s (t) in terms of Am and fm.

• What is the modulation index β and modify the above expression to include β.

• Derive an expression for whats called ”the peak frequency deviation” ∆f . Hint: ∆f is should really be called the ”peak instantaneous frequency deviation”

• Why is the spectrum of this sinusoidal modulation FM signal, ˜s (t) a line spectra?

• The Fourier series for ˜s (t) is:

where Jn  (β) is the nth  order Bessel function of the first kind.

Let fm  = 8kHz, and fc  = 100MHz:

–  Using Figure 3 sketch the spectra for β = 0.1

– If Am  = 1Volt, what approximate value of frequency sensitivity kf  would result in the spectral component at fc  being zero? You answer should use the correct units for kf.

Figure 3:  Some Bessel functions for use in question 3.

Question 4:

Consider the system shown in Figure 4.

Figure 4:  System to be considered in question 4

1.  Write an expression for y (t).

2.  Hence, or otherwise, derive (don’tjust quote) a time domain criteria on p (τ ) such that the collection of samples {y (kT)} are all ISI-free.

3.  Derive (don’tjust quote) the frequency domain version of the criteria derived in part 2. Let T = 1 and P (f), as shown in Figure 5(a), be the Fourier transform of p (τ):

i.e.  a triangular function of f.

Figure 5:  (a) Amplitude spectrum, jP (f)j, of pulse p (τ ) and (b) the cascade of two pulse shaping filters.

4.  Is this p (τ ) an ISI-free pulse?  Give reasons for your answer.

5.  Is the cascade of two of these, as shown in Figure 5(b), ISI-free?

6.  Suggest a simple modification to P (f) that would allow the cascade of two of them to be ISI-free.

7.  Why is this an important result?  Give an example of where it is commonly used.