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Selanus. wirdat madja EOtutli
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TLT-5206 COMMUNICATION THEORY — Final Exam 14.02.2013

Prepared by M.Valkama, no materials, no calculators

(Suomenkieliset kysymykset paperin toisella puolella)

1 Explain the concept of distortionless transmission. Given the transmit signal is x(f), and
the system is distortionless, how does the received signal y(f) 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 kind of
distortions are typically encountered in transmission systems, and how do they affect the
signal spectrum?

2 Explain the term and concept of random signals. How are they modeled? How random
signals are related to transmission and communications? Explain also the concepts of
white noise, Gaussian noise, stationary random signal, spectrum density, ergodic random
signal.

3; (a) A general bandpass signal can be expressed mathematically as
Xgp (1) = A(1) cOS(0t + P(£)) = x; (1) cos(Wgt) — x, (1) sin(mt)

Sketch an example waveform shape and spectrum of this kind of signal. In the above
expression, what do the guantities or functions A(f), Mf) and mc (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?

(b) Explain shortly the basic idea of freguency modulation (FM). Sketch also the
essential waveform shape and spectrum of the modulated signal (at principal levels) when
the modulating signal is a single sine-wave (freguency fw). Explain the basic pros and
cons of FM compared to linear modulations.

4. Present the time domain mathematical model for ideal sampling process. Given the
spectrum of a continuous-time signal, sketch (i.e., draw) also the corresponding spectrum
after ideal sampling. Based on that, formulate the basic reguirement in order to avoid
aliasing. Explain also the basic idea of reconstruction both in time and freguency
domains. Finally, tell the basic idea of sub-sampling principle in bandpass signal context.

5; (a) Explain shortly what is meant by (i) information and (ii) entropy. Explain also what
is meant in this context by channel capacity. (Here it is sufficient to keep the description
at a conceptual level.)

(b) Let's consider a carrier-modulated digital PAM/PSK/OAM system where the target
bit rate is 20 Mbits/s and the available transmission bandwidth around the center-
freguency is 6 MHz. Design the system at waveform level, i.e., determine reasonable
values for the key parameters (symbol rate, alphabet size, excess bandwidth, etc.).
Explain the thinking behind your design. How about the corresponding design in case of
baseband PAM system with the same target bit rate of 20 Mbits/s and similar physical
transmission bandwidth of 6 MHz?

Maximum points: 5 x 6 = 30p.