ECSE-303 SIGNALS AND SYSTEMS I
Assignment 2
ECSE-303 Problem Assignment 2
Problem 1 (30 marks)
Determine if the following systems are: (Justify your answers)
1. Memoryless
2. Time-invariant
3. Linear
4. Causal
5. Stable
6. Invertible
(a) y ( t ) = cos x (
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 5
ECSE-303 Problem Assignment 5
Due Monday March 17 before class
Problem 1 (30 marks)
Find the bilateral Laplace transforms of the following functions, giving the ROCs:
(a)
(b )
(c)
(d )
(e)
(f)
e 2 t u ( t )
e 2t
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 4
ECSE-303 Problem Assignment 4
Problem 1 (35 marks)
Using Fourier transforms, find the step response of a system with impulse response
h ( t ) = e t u ( t ) u ( t 2 )
Express the step response of this system in
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 6
ECSE-303 Problem Assignment 6
Problem 1 [10 marks]
You are given a system with impulse response h(t)=etu(t)
(a) is this system BIBO stable?
(b) You now hook the system up into a feedback system, as shown below.
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 3
ECSE-303 Problem Assignment 3
Due for Monday Feb. 16th before class in the ECSE 303 dropbox
Problem 1 (30 marks)
Suppose that a $1000 deposit is made at the beginning of each year in a bank account carrying
an a
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 5
ECSE-303 Problem Assignment 5
Due Monday March 17 before class
Problem 1 (30 marks)
Find the bilateral Laplace transforms of the following functions, giving the ROCs:
(a)
(b )
(c)
(d )
(e)
(f)
e 2 t u ( t )
e 2t
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 1
ECSE-303 Problem Assignment 1
Problem 1 (30 pts)
Write the following complex signals in (i) polar form and (ii) real/imaginary form
Polar form: x(t ) = r (t )e j ( t ) , r (t ), (t ) R for continuous-time signal
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 4
ECSE-303 Problem Assignment 4
Problem 1 (30 marks)
Using Fourier transforms, find the step response of a system with impulse response
h ( t ) = e t u ( t ) u ( t 2 )
Express the step response of this system in
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 3
ECSE-303 Problem Assignment 3
Problem 1 (30 marks)
Suppose that a $1000 deposit is made at the beginning of each year in a bank account carrying
an annual interest rate of r = 6%. The interest is vested in the a
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 1
ECSE-303 Problem Assignment 1
Problem 1 (30 pts)
Write the following complex signals in (i) polar form and (ii) real/imaginary form
Polar form: x(t ) = r (t )e j ( t ) , r (t ), (t ) R for continuous-time signal
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 6
ECSE-303 Problem Assignment 6
Due Wednesday April 2 before class
Problem 1 [10 marks]
You are given a system with impulse response h(t)=etu(t)
(a) is this system BIBO stable?
(b) You now hook the system up into
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 2
ECSE-303 Problem Assignment 2
Problem 1 (30 marks)
Determine if the following systems are: (Justify your answers)
1. Memoryless
2. Time-invariant
3. Linear
4. Causal
5. Stable
6. Invertible
(a) y ( t ) = cos x (
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 6
ECSE-303 Problem Assignment 6
Problem 1 [10 marks]
Compute the DC gain in dB, the peak resonance in dB, and the quality
causal filter with transfer function: H ( s ) =
Q of the second-order
1000
.
s + 2 s + 100
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 2
ECSE-303 Problem Assignment 2
Problem 1 (10 pts: 5, 5)
The following relationship is so useful in our studies that it is worth memorizing:
1 aN
Prove that a =
1 a
n =0
N 1
( a 1)
n
[Hint: multiply both sides by
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 4
ECSE-303 Problem Assignment 4
Problem 1 (30 marks)
Using Fourier transforms, find the step response of a system with impulse response
h ( t ) = te at u ( t ) a > 0 , a R e al
Express the step response of this sy
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 1
ECSE-303 Problem Assignment 1
Problem 1 (30 pts)
Write the following complex signals in (i) polar form and (ii) real/imaginary form
Polar form: x(t ) = r (t )e j ( t ) , r (t ), (t ) R for continuous-time signal
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 3
ECSE-303 Problem Assignment 3
Problem 1 (30 marks)
Consider the following second-order Butterworth filter:
The differential equation relating the input and output voltages of this RLC filter is
LC
d 2 y (t ) L d
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 5
ECSE-303 Problem Assignment 5
Problem 1 (25 marks)
Find the output y(t) of the system h ( t ) = e
2 t
u ( t ) for the anti-causal input x ( t ) = e t u ( t ) by
using the Laplace transforms.
Answer:
By conversio
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 1
ECSE-303 Problem Assignment 1
Due Monday Jan. 26 in the assignment box before the 14:35 class
Problem 1 (10 pts)
For the signal x(t) of the figure below, plot
x (t )
1
-2
2
t
(a) x(-t/2)
(b) x(-5t+1)
1/13
rev.2/
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 4
Problem 2 [20 marks]
Consider the causal differential system characterized by the differential equation
d 3 y (t )
d 2 y (t )
dy (t )
+6
+ 11
+ 6 y (t ) = x (t )
3
2
dt
dt
dt
(a) [10 marks must use Unilateral La
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 2
ECSE-303 Problem Assignment 2
Problem 1 (40 marks)
(A) Compute the Fourier series coefficients of the following periodic signal. Express the
magnitude and phase of the Fourier coefficients. Also plot them.
x(t )
ECSE-303 SIGNALS AND SYSTEMS I
Assignment 3
ECSE-303 Problem Assignment 3
Due Monday March 23 before class
Problem 1 (20 marks)
Find the Laplace transforms of the following functions either by direct integration or by using
properties of Laplace Transform
ECSE 303 Signals and Systems I
Midterm Test 2
ECSE-303 Signals and Systems I
Midterm Test 2
Winter 2007
Department of Electrical and Computer Engineering
McGill University
Use an ink pen
No calculator allowed
Problem 1 (20 marks)
a) The spectrum of a give
ECSE-303a Signals and Systems I
MID-TERM 2
Monday March3, 2008
Winter 2008
MID-TERM 2
ECSE-303a Signals and Systems I
Department of Electrical and Computer Engineering
McGill University
Monday March 3rd, 2008
18:30-20:30
Examiner:
Prof. Martin Rochette
As
Sample Midterm Test 2 (mt2s04)
Sample Midterm Test 2 (mt2s04)
Covering Chapters 4-5 and part of Chapter 15 of Fundamentals of Signals & Systems
Problem 1 (35 marks)
The following nonlinear circuit is an ideal full-wave rectifier.
+
vin ( t )
R
- v (t ) +
Sample Midterm Test 2 (mt2s02)
Sample Midterm Test 2 (mt2s02)
Covering Chapters 4-5 and part of Chapter 15 of Fundamentals of Signals &
Systems
Problem 1 (25 marks)
Consider the second-order, lowpass RLC Butterworth filter depicted below. The input voltag
Sample Midterm Test 2 (mt2s01)
Sample Midterm Test 2 (mt2s01)
Covering Chapters 4-5 and part of Chapter 15 of Fundamentals of Signals &
Systems
Problem 1 (30 marks)
(a) [10 marks] Consider the periodic signal x ( t ) depicted below. Give a mathematical ex
Sample Midterm Test 2 (mt2s03)
Sample Midterm Test 2 (mt2s03)
Covering Chapters 4-5 and part of Chapter 15 of Fundamentals of Signals & Systems
Problem 1 (30 marks)
The following nonlinear circuit is an ideal full-wave rectifier.
+
vin ( t )
R
- v (t ) +
ECSE-303a Signals and Systems I
MID-TERM 2
Monday February 2, 2009
Winter 2009
MID-TERM 2
ECSE-303a Signals and Systems I
Department of Electrical and Computer Engineering
McGill University
Monday March 2, 2009
18:30-20:30
Examiner:
Prof. Martin Rochette
ECSE-303a Signals and Systems I
MID-TERM 1
Monday February 2, 2009
Winter 2009
MID-TERM 1
ECSE-303a Signals and Systems I
Department of Electrical and Computer Engineering
McGill University
Monday February 2, 2009
18:30-20:30
Examiner:
Prof. Martin Rochet