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Konstantin, VY kovOtut. D

TLT-5206 COMMUNICATION THEORY — Mid-term exam 11.10.2011

 

(Finnish guestions on the other side.) No materials. Basic calculator OK. Prepared by J. Talvitie.

1. — Answer briefly to the following guestions and justify your answers:

a. Mention at least three reasons why modulation is used in communications systems.
(2p)

b. Describe differences between Fourier series and Fourier transformation concepts.
What kind of use case limitations there are for exploiting the concepts? Which one
would you choose to study spectral content of a sinusoidal signal? (2p)

c. What is the connection between an impulse response and a transfer function in case
of LTI (linear time-invariant) systems? What can you say about the amplitude
response (consider two-sided spectrum) if you know that the impulse response is
real valued? (2p)

2. = Explain the concept of distortionless transmission. Given the transmit signal is x(t), and the
system is distortionless, how does the received signal y(t) depend on the transmit signal and
the properties of the system? Based on this, what kind of transfer function, and thereon
amplitude- and phase responses, does a distortionless system have? What kinds of distortions
are typically encountered in transmission systems, and how do they affect the signal
spectrum? (6p)

3. — What is meant by the concept random signal? Why one usually needs to consider such
random signals in analyzing and modeling communication systems? In this context, explain
briefly what is meant by the following terms or concepts (a) stationarity (strict-sense vs.
wide-sense), (b) autocorrelation, (c) white noise, (d) Gaussian noise. (6p)

4. — A general bandpass signal can be expressed mathematically as
Xgp 1) = A(N)c0s(0f + P(1)) = x, (1) coS(0t) — x, ()sin(wr)

Sketch an example waveform and the corresponding spectrum of this kind of signal. In the
above expression, what do the guantities or functions A(f), Xf) and ax (or fc) represent
physically? Sketch also the spectrum of the corresponding lowpass eguivalent signal. What's
the time domain expression for this lowpass eguivalent signal and how does it describe the
waveform characteristics of the original bandpass signal? (6p)

 

5. — (a) Explain what is meant by a Hilbert transformer and how is it related to SSB modulation.
Explain also how a real-valued signal can be transformed into an analytic signal (i.e.,
into a signal which consists of only the positive freguency components of the original
signal) using a Hilbert transformer. How is this related to SSB modulation? (3p)

(b

D

Compare different linear modulation methods (AM, DSB, SSB and OAM) with respect
to transmission bandwidth and power efficiency (mathematical analysis is not reguired
here). (3p)