Ee320a Tut1
Ee320a Tut1
Ee320a Tut1
in) 1
EE320A
Tutorial 1
Date: 7th Aug. 2015
1 v1 (t)
A B vo (t) = dv1 (t)/dt
+
2F d
vi (t) = 3 cos(6t) i(t) dt
(volts)
2. Consider the system shown in Figure 1. Assume that the current in branch
AB is zero. The voltage at point A is v1 (t).
(a) Find out the time domain expression that relates v1 (t) and vi (t).
(b) Using the Fourier transform, find out the relation between V1 (f ) and
Vi (f ).
(c) Find the relation between Vo (f ) and Vi (f ).
(d) Compute the power when the output voltage vo (t) is applied across
a 1 ohm resistor.
(n)
3. Consider a complex-valued signal g(t). Let g1 (t) = g (t). Let g1 (t)
denote the nth derivative of g1 (t). Consider another signal g2 (t) = g (n) (t).
(n)
Is g2 (t) = g1 (t)? Justify your answer using Fourier transforms.
4. Prove the following using the Schwarzs inequality:
Z
|G(f )| |g(t)| dt
t=
Z
dg(t)
|j 2f G(f )| dt dt
t=
Z 2
2
d g(t)
(j 2f ) G(f ) dt2 dt.
t=
K Vasudevan Faculty of EE IIT Kanpur (vasu@iitk.ac.in) 2
g(t)
2 1 1 2
Evaluate the three bounds on |G(f )| for the pulse shown in Figure 2.
2(t)
(t 3T /2)
t
0 T /2 T
(a) Compute the real Fourier series representation of gp (t). Give the
expression for the coefficient of the nth term.
(b) Compute the Fourier transform of gp (t).