Fundamentals of Signals Overview
ContinuousTime Unit Step
Unit step
u(t)
Switches
1
Unit impulse
t
Relationships
u(t)
0
1
t<0
t>0
Sometimes known as the Heaviside function
Discontinuous at t = 0
u(0) is not dened
Not of consequence because it is
Lesson 15: Solving Vector Problems in Two Dimensions
We can now start to solve problems involving vectors in 2D.
We will use all the ideas we've been building up as we've been studying vectors to be able to
solve these questions.
The majority of questio
Lesson 12: Gravity
Aristotle
From the time of Aristotle (384322 BC) until the late 1500s, gravity was believed to act differently on
different objects.
This was based on Aristotle's observations of doing things like dropping a metal bar and a
feather at
Lesson 13: Vectors in One Dimension
Up to this point we have been focusing on the number crunching sort of questions you can do in
physics.
In this chapter the focus will start to be shifted toward more complicated problems that might
not always be solve
Lesson 14: Vectors in Two Dimensions
Two dimensional problems are a little tougher, because we are no longer just lining up collinear vectors
and doing quick math.
Instead, we need to pay attention to how 2D vectors form a more complex (but not very
comp
Lesson 17: Projectiles Launched Horizontally
The study of projectile motion brings together a lot of what you have learned in the past few seconsti.
You need to know about gravity, velocity, acceleration, and vector components to be able to
fully underst
Lesson 18: Projectile Motion at an Angle
To do questions involving objects launched from the ground upwards at an angle (like kicking a
football up into the air and watching it as it arcs in the air and comes back down), you need to add a
few more steps t
Overview of Convolution Integral Topics
Impulse Response
Impulse response dened
x(t)
Several derivations of the convolution integral
h(t)
y(t)
Recall that if x(t) = (t), the output of the system is called the
impulse response
Relationship to circuits
TwoPort Networks
OnePort Networks
Denitions
Impedance Parameters
+
Admittance Parameters
v
Hybrid Parameters
i1

Transmission Parameters
OnePort
Network
i'1
A pair of terminals at which a signal (voltage or current) may
enter or leave is called
Overview of Bode Plots
Prerequisites and New Knowledge
Review of transfer functions and bode plots
Prerequisite knowledge
Piecewise linear approximations
Ability to use transfer functions for steadystate sinusoidal circuit
analysis
Firstorder terms
Second Order Filters Overview
Prerequisites and New Knowledge
Whats dierent about second order lters
Prerequisite knowledge
Resonance
Ability to perform Laplace transform circuit analysis
Standard forms
Ability to solve for the transfer function of a
Practical Analog Filters Overview
Ideal Filters
Types of practical lters
Lowpass
Highpass
1
Filter specications
Tradeos
c
1
c
Bandpass
Many examples
Notch
1
c
Bandstop
1
1
c1
c2
c1
c2
There are ve ideal lters
Lowpass lters pass low frequencies: < c
Analog Filters Overview
Introduction to Filters
Ideal lters
H(s)
x(t)
Bode plots
Firstorder lters
x(t) = A cos(t + )
Active & passive lters
yss (t) = AH (j ) cos (t + + H (j )
Secondorder lters
In general, H (j ) will vary with
Resonance
Filt
Transfer Functions
Prerequisite and New Knowledge
Transfer functions dened
Prerequisite knowledge
Linearity and time invariance dened
Ability to nd Laplace transforms of signals
Examples
Ability to nd inverse Laplace transforms
Sinusoidal steadysta
Overview of Laplace Transforms for Circuit Analysis
Prerequisite and New Knowledge
Passive element equivalents
Prerequisite knowledge
Review of ECE 221 methods in s domain
Ability to nd Laplace transforms of signals
Examples
Ability to nd inverse Lap
Overview of Laplace Transform Topics
Laplace Transform Motivation
Denition
vs(t)
Region of convergence
+
Linear
Circuit
vs(t)
Useful properties
t
vo(t)

Inverse & partial fraction expansion
Distinct, complex, & repeated poles
In ECE 221, you learne
Lesson 8: Velocity
Two branches in physics examine the motion of objects:
Kinematics: describes the motion of objects, without looking at the cause of the motion
(kinematics is the first unit of Physics 20).
Dynamics: relates the motion of objects to the