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 fall back into our routine of coding in MATLAB and we are
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). (a) Find the simplest piecewise
math form for p(t).
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. Below are the plots of two continuous convolution pro
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, plot each st and S f . (a) st 2 ut 001 ut 001 , (b) st
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 the following functions:
(a)
g(t),
(b) g(t),
(c) g(t 4),
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. Continuous convolution is often a
challenging concept, a
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 obtaining the frequency response and determining
poles
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 this Project, we will use MATLAB to simulate how digital
d
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) Signal Spectrum. A mathematical operation called the
Di
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
0 ,
else
Plot | X(f ) | over a Hz frequency range larg
Turn-In Assignment 6: DUE - Wed, 16 Oct 2013
ECE 301 - Fa2013
Problem 1.
1
(10 pts)
A system impulse response is given by h(t) = 50 e 10 t sin( 200 t) u(t).
response H() at = 300 rad/sec can be written in two forms:
H( = 300) =
A+jB
D+jE
=
The rad/sec fre
ECE 301 - Spring 2012
1
Sec. 001 - Test 2 Answers
1. Let a component h(t) of a larger system have impulse response h(t) = e 10 t u(t). With G = 30,
let the component h(t) be connected to form the larger system shown in the conguration below:
x(t)
+
G
y(t)
ECE 301 - 001
Spring 2017
1
Test 1 w/Solutions
1. Let a linear system with input x(t) and output y(t) be described by the ODE below:
d2
d
d
y(t) + 20 y(t) + 15, 890 y(t) = 5 x(t) + 50 x(t)
2
dt
dt
dt
(a) Compute the simplest real-valued mathematical form
ECE 301 - 001
Spring 2017
1
Test 2 w/Solutions
1. A circuit with transfer function H(s) =
+
x(t)
Y (s)
and R = 50 and L = 0.01 H is shown below:
X(s)
+
R
y(t)
L
(a) Let A, B, and D be constants (any of which could be zero). Then H(s) can be written as
As
Turn-In Assignment 1: 21 Jan 2015
ECE 301 - Sp2015
1
1. Let a function g() be defined by the following piecewise math form:
g() =
(
2 5, 0 4
0, else
Let the time-domain function p(t) be given by p(t) = g(32 t). (a) Compute the simplest piecewise
math form
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 path:
reected path:
Ad = 0.80, distance = d = 5.1 m;
A1
ECE 301 - Fa2013
Notes Set 11: Sampling and Reconstruction
1
INTRODUCTION
Many components of modern media systems are implemented using digital signal processing.
Among these applications are cell phones, audio CDs, video DVDs, digital television, digital
ECE 301 - Fa2013
Notes Set 8: Poles and Zeros
1
INTRODUCTION
We have seen in earlier notes that once we have the system transfer function H(s), we can
often nd the frequency response H(f ) by a simple substitution of variables. However, the
transfer funct
ECE 301 - Fa2013
Notes Set 6: Frequency Response
1
INTRODUCTION
In Notes Set 5 we examined the frequency content, or spectrum, of time-domain signals.
In this set of Notes we will study the ability of the system to propagate or attenuate the
frequencies o
ECE 301 - Fa2013
Notes Set 7: Frequency Domain Output
1
INTRODUCTION
In the previous Notes Sets we examined the Frequency Response of a linear system, but
we did not emphasize nding the time-domain output of the system. Now we study the
problem of obtaini
ECE 301 - Fa2013
Notes Set 2: Continuous Convolution I
1
INTRODUCTION
We have previously studied the impulse response of a linear system in Notes Set 2. By
denition, the impulse response h(t) is the response (output) of the system when the input
is an imp
ECE 301 - Fa2013
Notes Set 3: Continuous Convolution II
1
INTRODUCTION
In Notes Set 2 we found that the output of a continuous system with impulse response h(t)
was given by the convolution of h(t) with the analog input x(t). The convolution integral
was
ECE 301-Fa2013
Notes Set 14: Digital Convolution
1
INTRODUCTION
It was seen previously that continuous-time (analog) convolution arises naturally when we
want to nd the response of an analog system to a specic analog excitation. We now will
consider the o
ECE 301 - Fa2013
Notes Set 13: Digital Signal Processing
1
INTRODUCTION
In the rst part of Notes Set 11 we examined the problem of sampling an original analog
signal to acquire signal samples. This sequence of digital samples may now be considered
as a Di
ECE 301 - Fa2013
Notes Set 10: Communications Systems
1
INTRODUCTION
One area which uses a great deal of linear systems theory is Communications. The area
of Communications is very broad and is divided among specialities such as Amplitude
Modulation (AM),
ECE 301 - Fa2013
Notes Set 9: Analog Filter Design
1
INTRODUCTION
One of the most important applications of the s-plane is Analog Filter Design. Analog
lter design combines the previous concepts of transfer function, frequency response, and
poles/zeros an
ECE 301 - Fa2013
Notes Set 1: Impulse Response
1
INTRODUCTION
You have probably studied basic circuits in an earlier course like ECE 211. Typical problems
at that level of investigation might have been to nd the output of a circuit in response to
a partic
ECE 301 - Fa2013
Notes Set 4: Transfer Functions
1
INTRODUCTION
In this set of Notes we will study some very useful properties of the the Laplace Transform
and the s-domain, which will result in determining the Transfer Function of a system. We
will see t
ECE 301 - Fa2013
Notes Set 5: Signal Spectrum
1
INTRODUCTION
The previous sets of Notes have examined the properties of systems in the time domain.
In that regard, you could think of a time domain signal g(t) as describing how the signals
voltage or curre
Basic Computations and Plots
Tutorial Project Notes
1
1. INTRODUCTION
This set of Project Notes contains examples of some basic computations and plots. The
specific topics are plotting and scaling sinusoids, exponentials, and computing products.
These top
Solutions - Set 5: Transfer Functions
ECE 301 - Fa2016
1
5-1. A system has impulse response h(t) = 10, 000 e 5000 t u(t), input x(t), and output y(t).
(a)
Compute the transfer function H(s).
(b) Using Laplace transforms and partial fraction expansion, com
1
Solutions - Set 1: Impulse Response
ECE 301 - Fa2016
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 functions:
(a)
g(t),
(b)
g(t),
(c)
g(t 4),
(d)
g(4 t)
ECE 301 - Fa2016
1
Problem Set 13: Sampling Theorem
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 waveform s (t) be given by
X
s (t) =
(t m Ts )
(p1)
m=
S
Solutions - Set 13: Sampling Theorem
ECE 301 - Fa2016
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 waveform s (t) be given by
s (t) =
X
(t m Ts )
(p1)