Introduction
In this project, we will ultimately be refreshing our previous knowledge of MATLAB
functions, coding styles, and processes. By going through a few introductory problems, we are
able to fa
ECE 301 - Spring 2012
1
Test 1 - Sec.1 w/Answers
1. Let a function g() be dened by the following piecewise math form:
g() =
2 , 2 2
0,
else
Let the time-domain function p(t) be given by p(t) = g(3 2 t
Solutions - Set 3: Continuous Convolution I
ECE 301 - Sp2012
1
3-1. A system has an impulse response given by h(t) = e 2 t u(t). Let this system now have input
given by x(t) = 5 (t 1) 3 (t 4). Compute
Turn-In Assignment 2: DUE - Mon, 9 Sept 2013
ECE 301 - Fa2013
1
Problem 1.
Suppose a wireless transmitter is sending data to a receiver in the reection environment described
by the following:
direct p
Introduction
In this project, we will be using MATLAB to explain, compute, and plot continuous
convolution functions. We began by working through a few introductory problems found within
the note sets
ECE 301
Detailed Solutions - Set 8 : Signal Spectrum
1
8-1. Several signals st are given below. For each signal use the Fourier transform to compute the mathematical form for the spectrum S f . Also,
ECE 301 - Fa2017
1
Assignment 9 Solutions - 6 Nov 2017
Problem 1.
Let a baseband rectangular pulse g(t) at a transmitter be given by
g(t) =
(
t 0.5(10)5
10 ,
0,
else
In the following plots, use t
Solutions - Set 13: Sampling Theorem
ECE 301
1
13-1. This problem helps you derive the Fourier transform of the infinite series of impulses in
the time-domain. Let the periodic impulse-sampling wavefo
11-1.
1
Solutions - Set 11: Communications Systems
ECE 301
Plot the magnitude spectrum | X(f ) | if x(t) is given by
x(t) =
DETAILED
(
5 cos(107 t) ,
0,
|t| 5(10)7 sec
else
SOLUTION:
Note that the wav
ECE 301
Notes Set 16: Z-Transforms
1
INTRODUCTION
The Z-Transform is the frequency-domain analytical tool for digital signal processing
systems. It serves a purpose for DSP systems similar to the purp
ECE 301
1
Problem Set 15: Digital Convolution
h
i
15-1. A discrete system has the impulse response h[m] = (0.9)m u[m] u[m 4] . The system
receives the input
x[m] = 2 u[m 1] 2 u[m 2] u[m 4] + u[m 5]
Pl
1
Solutions - Set 1: Impulse Response
ECE 301
1-1. Let a function g() be defined by the following piecewise form:
(
g() =
2, 0 3
0,
else
Find the simplest math form for each of the following function
1
Solutions - Set 12: Sampling and Reconstruction
ECE 301
12-1. An analog signal x(t) = e 5 t u(t) is sampled using a sampling interval Ts seconds. The
digital signal which results can be written in t
1
Solutions - Set 15: Digital Convolution
ECE 301
h
i
15-1. A discrete system has the impulse response h[m] = (0.9)m u[m] u[m 4] . The system
receives the input
x[m] = 2 u[m 1] 2 u[m 2] u[m 4] + u[m 5
1
Turn-In Assignment 3: 8 Sept 2017
ECE 301 - Fa2017
Problem 1.
Let a system have unit step input x(t) = u(t) and output step response y(t) = yu (t), where
h
yu (t) =
i
1 e 50 t u(t)
(p1)
Now let a 2
ECE 301 - 001
1. Let R and
Fall 2017
1
Test 2 w/Answers
L have the values R = 2000 and L = 10 5 H in the circuit below:
+
vi (t)
vo(t)
R
R
+
L
R
Define the transfer function as H(s) = Vo (s)/Vi (s). T
ECE 301-002 Fall 2017
1
Test 3 w/Answers
1. Let H(s) be an N = 4th-order lowpass
Butterworth
filter
with half-power frequency B = 800
rad/sec. The voltage signal x(t) = cos 700 t + cos 900 t is inpu
ECE 301-002
Fall 2017
1
Test 3 w/Answers
1. A second-order analog filter has the block-diagram level implementation below:
A(s)
2
6
, B(s) =
s
s
A(s) =
G
X(s)
K=4, G =5
B(s)
K
+
Y(s)
Y (s)
N2 s 2 +
ECE 301-001
Fall 2017
1
Solutions - Test 1
1. Let a function g() be given by the following:
g() =
(
e 0.5 cos() ,
0,
04
else
(p1)
Let p(t) = g(2 0.5 t). (a) Compute the simplest piecewise math form fo
ECE 301 - 002
Fall 2017
1
Test 2 w/Answers
2s + 3
.
s2 + 19 s + 60
If the input to the system is x(t) = 3 e 2 t u(t), then the output for t 0 can be written as
1. Let the transfer function of a system
PROJECT GOAL
The goal of this project was to utilize MATLAB to simulate the input x(t) and
resulting output y(t) using numerical methods. This allowed us to see how first
order RC and second order RLC
ECE 301 - 002
Fall 2017
1
Test 1 w/Answers
1. Let a linear system with input x(t) and output y(t) be described by the differential equation
d2
d
y(t) + 12 y(t) + 2536 y(t) = 500 x(t)
2
dt
dt
(a) Compu
Solutions - Set 7: Frequency Response
ECE 301
7-1.
1
Let the impulse response h(t) of an RC-circuit be given by
h(t) = K e b t u(t),
where
1
RC
b =
Use the Fourier transform integral to compute the fr
1
Solutions - Set 2: Step Response
ECE 301
2-1. With D a constant, let a Laplace transform expression G(s) be given by
D
s(s + b)
G(s) =
Use Partial Fraction Expansion to show that an equivalent form
Turn-In Assignment 1: DUE - Fri, 30 Aug 2013
ECE 301 - Fa2013
1
Problem 1.
Let a function g() be dened by the following piecewise form:
2 , 0 3
0,
else
g() =
Find the simplest math form for each of th
ECE 301 Project Notes
Continuous Convolution
1
1. INTRODUCTION
This set of Project Notes accompanies class Notes Sets 2 and 3, and contains MATLAB
examples to help understand continuous convolution. C
ECE 301 Project Notes
Poles/Zeros and Frequency Response
1
1. INTRODUCTION
This set of Project Notes accompanies the class lecture Notes Sets 6 and 8, which study
analytical (mathematical) methods for
1
Digital Communication System Simulation
ECE 301 Project Notes
1. INTRODUCTION
This set of Project Notes accompanies class Notes Set 10 which studies modulation and
communications. Specically, in thi
ECE 301 Project Notes
Spectrum Computation Using the FFT
1
1. INTRODUCTION
This set of Project Notes accompanies the class Notes Set 5, which studies theoretical properties of the continuous (analog)
Problem 1.
1
Turn-In Assignment 5: DUE - Wed, 9 Oct 2013
ECE 301 - Fa2013
(10 pts)
A time signal x(t) having Fourier transform X(f ) is given by
x(t) =
6 cos(439.81 t) + 2 sin(1570.8 t), 0.025 t 0.025
ECE 301
1
Problem Set 1: Impulse Response
1-1. Let a function g() be defined by the following piecewise form:
(
g() =
2,
0,
03
else
Find the simplest math form for each of the following functions:
(a
1
Solutions - Set 1: Impulse Response
ECE 301
1-1. Let a function g() be defined by the following piecewise form:
(
g() =
2, 0 3
0,
else
Find the simplest math form for each of the following function
9-1.
1
Solutions - Set 9: Poles and Zeros
ECE 301
Let an analog filter have the transfer function given by
H(s) =
s2
s 2 + 106
+ 100 s + 106
(a) Compute the s-plane poles and zeros of this filter. (b)
1
Solutions - Set 4: Continuous Convolution II
ECE 301
4-3. Let a system have impulse response h(t) and input x(t) given by
h(t) =
(
5, 0 t 1
,
0, else
x(t) =
(
3, 0 t 1
0, else
Compute the analytical
1
Solutions - Set 8: Frequency Domain Output
ECE 301
8-1. The output y(t) of a linear system having impulse response h(t) and input x(t) is given by
the convolution integral:
Z
y(t) =
h( ) x(t ) d
=