(a) (i) Define the term ‘signal’ as used in communication.
(ii) State, with reasons, whether or not the signal x(t) = cos 2t + cos5t belongs to each of
the classes: deterministic, complex, periodic, energy
[5 marks]
(b) (i) Obtain the Complex Exponential Fourier Series of the signal
g t f t f t o o ( ) = 1+ cos 2p + sin 4p
(ii) Plot the Amplitude, Phase and Power Spectra of the signal
[5 marks]
(c) (i) A signal q(t) has a Fourier TransformQ( f ) . Obtain the Fourier Transform, G( f ) of
the signal g(t) defined by g(t) q(t) cos(2 f t) o = p in terms ofQ( f ) , where o f is constant.
(ii) Using suitable sketches illustrate the spectral difference between q(t) and g(t) .
[3 marks]
(d) An exponential pulse V (t) i may be defined in the time domain by

<
³
=
–
0, 0
, 0
( )
t
e t
V t
at
i with a being positive and real valued
(i) Determine the total normalized energy of V (t) i
(ii) Determine the Fourier Transform of the exponential pulse.
[3 marks]
(e) The pulse in (d) is applied to a network of impulse response, h(t) (1 exp[ ])u(t) CR
= – – t .
Determine the energy spectral density function of the output, V (t) o .
[4 marks]

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