Chapter 13
Control Systems
13.1
The trouble with open loop control
Consider a system, which we will call the plant, with transfer function Gp (s), input x(t), and output
y (t). The output of the plant in the s-domain is Y (s) = X (s)Gp (s). We might ask w
Chapter 8
Sampling and Periodicity
8.1
Sampling time-domain signals
Quite early in ECE2026, we introduced the notion creating a discrete-time signal by sampling a continuoustime signal, along with a convenient slight abuse of notation: x[n] = x(xTs ), whe
Chapter 10
Laplace Transforms (Fall 2013)
This chapter, in its present form, was primarily written by Prof. Magnus Egerstedt, with some modications
by Aaron Lanterman. It is highly preliminary. Be warned that some of the presentation diers in style
from t
Chapter 12
Second-order Step Responses
(Under construction. A lot of construction.)
12.1
Second-order lowpass lter
A second-order lowpass transfer function may be written as
H2LP (s) =
The poles are located at n (
12.1.1
2
n
2
= 2 nn
.
2
2
s2 + 2n s + n
Chapter 7
Modulation
In this chapter, we will present a simplied story of how AM radio works. This is a practical application
that will let us introduce a few new Fourier properties in a concrete context while also reviewing some of
the Fourier theory we
Chapter 11
Second-order Frequency Responses
There are two common ways of notating the denominators of system functions of second-order LTI systems:
2
D(s) = s2 + 2n s + n = s2 +
n
2
s + n .
Q
(11.1)
In both notations, n represents the systems undamped nat
Chapter 9
Correlation and Matched Filtering
Suppose we measured a waveform that had the form of a signal corrupted by additive noise
x(t) = sk (t) + n(t),
(9.1)
where s1 , s2 , etc. represent dierent kinds of signals, which we call templates, that we are
Chapter 6
Fourier Transforms
6.1
Motivation
Take another look at the Fourier analysis integral and Fourier series summation:
ak =
1
T0
T0 / 2
x(t) exp j
T0 /2
x(t) =
ak exp j
k=
2
kt dt,
T0
2
kt .
T0
We have always thought of x(t) as being a periodic sign
Chapter 4
More on Continuous Time
Convolution
We begin by recalling the denition of an impulse response. If the input to a system is an impulse; i.e.,
x(t) = (t), then we call the corresponding output the impulse response and denote it as y (t) = h(t). We
Chapter 5
Review of Fourier series
Before we present Fourier transforms in general, we will review Fourier series, since they provide an intuitive
springboard from which we can later study Fourier transform, which extend the idea of Fourier series to
sign
EE 3084: Linear Systems Theory(Signals and Systems)
School of Electrical and Computer Engineering
Georgia Institute of Technology
Professor William D. Hunt
Problem Set #1
Handed out: January 9, 2014
Due:
January 16, 2014
1.
Name and describe 3 systems.out
Chapter 3
Why Are LTI Systems So Important?
This chapter explores the question: why are LTI systems so interesting?
This chapter is about the big ideas. It is basically a 30,000 feet view of the the rst half of this text
(which sets the stage for the seco
Chapter 2
What are Systems?
In the previous chapter, we described signals as functions mapping from some domain, such as time or space,
to some range, such as air pressure, voltage, or light intensity.
We will abstract systems as mappings from one set of
Chapter 1
What are Signals?
Let us begin by considering what we mean by the term signals, in the sense of a course with a name like
signals and systems.
Mathematically, we abstract signals as functions that map a domain to a range. In particular, we are
i