EE 220: Signals, Systems & Networks
Tutorial-1
Basic operations on Signals
Q. 1 Determine whether or not each of the following signal is periodic. If a signal is periodic,
specify its fundamental period.
a) z(t) = sin(3t) + sin(2t)
b) z(t) = sin(3t) + sin

EE 220: Signals, Systems & Networks
Tutorial-8
Properties of Fourier Series and Transform
Q. 1 Suppose that a continuous time periodic signal is the input to an LTI system. The signal
has a FS representation
P
x(t) =
|k| e jk(/4)t
k=
where is a real numbe

EE 220: Signals, Systems & Networks
Tutorial-9
Sampling theorem
Q. 1 (a) A signal x(t) = 5 sinc2 (5t) + cos(20t) is sampled at a rate of 10 Hz. Find the spectrum
of the sampled signal. Can x(t) be reconstructed by low-pass filtering the sampled signal?
(b

EE 220: Signals, Systems & Networks
Tutorial-5
Differential equations
Q. 1 (a) In the circuit shown in Fig. 1 there are three meshes.
Write differential representation for each of the meshes using KVL assuming zero initial
capacitor voltage and zero initi

EE 220: Signals, Systems & Networks
Tutorial-7
Fourier Series and Transform
Q. 1 Find the Fourier series coefficients of the following periodic square wave shown in Figure 1:
1 i f |t| < T 1
x(t) =
0 i f T 1 < |t| < T
2
Figure 1: Square Wave
Sol.1.
The

EE 220: Signals, Systems & Networks
Tutorial-4
LTI System Properties
Q1: (a) Let u1 (t) be the impulse response of the differentiation system. Using this system, show
that if y(t) = x(t) h(t), then y (t) = x (t) h(t) . Prove the same mathematically and al

EE 220: Signals, Systems & Networks
Tutorial-8
Properties of Fourier Series and Transform
Q. 1 Suppose that a continuous time periodic signal is the input to an LTI system. The signal
has a FS representation
P
x(t) =
|k| e jk(/4)t
k=
where is a real numbe

EE 220: Signals, Systems & Networks
Tutorial-7
Fourier Series and Transform
Q. 1 Find the Fourier series coefficients of the following periodic square wave shown in Figure 1:
1 i f |t| < T 1
x(t) =
0 i f T 1 < |t| < T
2
Figure 1: Square Wave
Q. 2 Consid

EE 220: Signals, Systems & Networks
Tutorial-6
Difference equations
Q. 1 Write the system function shown in figure (a) and (b) in the form of difference equation,
Where D is the delay element which is given by
x(n-1)
x(n)
D
Figure 1
(a)
x(n)
bo
b1
b2
B
A

EE 220: Signals, Systems & Networks
Tutorial-5
Differential equations
Q. 1 (a) In the circuit shown in Fig. 1 there are three meshes. Write differential representation for
each of the meshes using KVL assuming zero initial capacitor voltage and zero initi

EE 220: Signals, Systems & Networks
Tutorial-6
Difference equations
Q. 1 Write the system function shown in figure (a) and (b) in the form of difference equation,
Where D is the delay element which is given by
x(n-1)
x(n)
D
Figure 1
(a)
x(n)
bo
b1
b2
B
A

EE 220: Signals, Systems & Networks
Tutorial-4
LTI System Properties
Q1: (a) Let u1 (t) be the impulse response of the differentiation system. Using this system, show
that if y(t) = x(t) h(t), then y (t) = x (t) h(t) . Prove the same mathematically and al

EE 220: Signals, Systems & Networks
Tutorial-3
Convolution
Q1: x(t) = u(t 3) u(t 5) and h(t) = e3t u(t). Compute y(t) = x(t) h(t).
Sol 1:
y(t) = h(t) x(t) =
R
=
h()x(t )d
Figure 1 shows the plots of h(), and x(t ) for different ranges of t.
1.5
h(tau)
1
0

EE 220: Signals, Systems & Networks
Tutorial-3
Convolution
Q1: x(t) = u(t 3) u(t 5) and h(t) = e3t u(t). Compute y(t) = x(t) h(t).
Q2: (a) Consider an LTI system with input and output related through the equation
Rt
y(t) = e(t) x( 2)d. What is the impulse

EE 220: Signals, Systems & Networks
July - Nov 2015
Tutorial-1
Basic operations on Signals
Q. 1 Determine whether or not each of the following signals is periodic or not. If periodic, then
find its fundamental period.
1. z(t) = sin(3t) + sin(2t)
2. z(t) =