ECE 219: Signal, System & Control

Tutorial Sheet 4 –Fourier Transform & Sampling

Submission date: April 06, 2015

1) The signals in Fig. Q1 (a)-(c) are modulated signals with carrier . Find the Fourier

transforms of these signals using appropriate properties of the Fourier transform. Sketch the

amplitude and phase spectra for (a) and (b).

Figure. Q1)

2) Define

. Given the Fourier transform

, find the

Fourier transform of the signal with being some constant, by making use of

the duality property of the Fourier transform.

3) If a signal and the

be a train of pulses. This signal is depicted in the figure below

4)

5)

a) Compute the Fourier series of .

b) What is the spectrum of the sampled signal .

(c) Explain if we can recover the from ?

d) If is passed through an ideal lowpass filter of bandwidth 100 Hz and unit gain what is

the output? What is the filter output if the bandwidth is B Hz, where 100<B<150? What happens

if B>150?

****