1. TELE3113 Analogue and Digital Communications
Tutorial 1
1. Consider a continuous time signal , defined for all time .
(a) Sketch , showing all important features.
(b) Find the Fourier transform of this signal
(c) Sketch the magnitude and phase spectra of
2. Find the Fourier transform of . Hence sketch the magnitude and
phase spectra
3. A Signal consists of two sinusoidal components,
, for all
where the frequencies and are constant
(a) Write as the product of two sinusoidal functions
(b) Hence, sketch when
(c) What is the envelope of , with respect to ?
(d) Is always a periodic signal? Explain under what conditions the signal is periodic.
4. Determine the Fourier transform of a rectangular pulse

2. 5. Using the result of question 4, find the Fourier transform of a truncated sinusoidal signal (that is,
one observed for a finite time )
by following the steps:
(a) Show that can be expressed as
that is, as the product of a shifted version of the rectangular pulse, multiplied by the sinusoid
(b) Use the Fourier shift theorem to find the Fourier transform of
Sketch the magnitude spectrum of this signal
(c) Using the convolution theorem, write down the Fourier transform of the truncated sinusoidal
signal .