6.189 IAP 2011: Recursion Notes
Recursion: (denition) noun. See recursion.
Recursion: Formal Denition: An algorithmic technique where a function, in order to accomplish a task, calls
itself with some part of the task.
Recursive solutions involve two majo
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.243j (Fall 2003): DYNAMICS OF NONLINEAR SYSTEMS
by A. Megretski
Problem Set 7 Solutions1
Problem 7.1
A stable linear system with a relay feedback excitation
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.243j (Fall 2003): DYNAMICS OF NONLINEAR SYSTEMS
by A. Megretski
Problem Set 6 Solutions1
Problem 6.1
For the following statement, verify whether it is true o
Single source shortest path problem
2
4
4
2
2
1
1
2
3
4
6
2
3
3
5
Find the shortest path from a source node to
each other node.
Assume: (1) all arc lengths are non-negative
(2) the network is directed
2
(3) there is a path from the source
node to all othe
6.033 Spring 2009, Quiz 2 Solutions
I
Page 2 of 17
Reading Questions
1. [8 points]: Based on the Unison paper entitled How to Build a File Synchronizer, by Trevor
Jim et al., state whether each of the following is true or false.
(Circle True or False for
LNA Design Example
7
6
5.5
5
4.5
c = -j0
4
3.5
3
The design yields
Achievable values as
a function of Q under
the constraints that
1
= wo
(Lg+Ldeg)Cgs
gm
L = Rs
Cgs deg
6.5
Noise Factor Scaling Coefficient
In our previous design
example, we picked the Q
f
Eulerian Walks in Directed Graphs in O(m) time.
Step 1. Create a breadth first search tree into node
1. For j not equal to 1, put the arc out of j in T
last on the arc list A(j).
Step 2. Create an Eulerian cycle by starting a walk
at node 1 and selecting
VCO Design for Narrowband Wireless Systems
Zin
From Antenna
and Bandpass
Filter
PC board
trace
Zo
RF in
Package
Interface
Mixer
IF out
To Filter
LNA
LO signal
VCO
Reference
Frequency
Frequency
Synthesizer
Design Issues
- Tuning Range need to cover all fre
Voltage Controlled Oscillators (VCOs)
L1
Vout
Cvar
L
L2
Vout
Vout
M1
M2
Vs
Vbias
Cvar
M1
C1
V1
Vcont
Ibias
Ibias
Cvar
Vcont
Include a tuning element to adjust oscillation frequency
- Typically use a variable capacitor (varactor)
Varactor replaces (part of
Image Reject Mixer, Review
RF
r(t)
y(t)
Balanced
modulator
-90o phase
shifter
Local Oscillator
+
LPF or
BPF
IF Output
-90o phase
shifter
Balanced
modulator
z(t)
^
z(t)
Rather than filtering out the image, we can cancel it out using an image
rejection mixe
A Simple Bucket-based Scheme
Let C = 1 + max(cij : (i,j) A); then nC is an upper
bound on the minimum length path from 1 to n.
RECALL: When we select nodes for Dijkstra's
Algorithm we select them in increasing order of
distance from node 1.
SIMPLE STORAGE
Lecture 11
Sam Madden
Network Layer
Today: Network layer.
Job of network layer is to nd and forward packets along a path between sender and
receiver in a multi-hop network.
Show example network:
"routers"
Network layer interface
Two main jobs:
Forwarding
Starting Point
Assume lexical analysis has produced a sequence
of tokens
Each token has a type and value
Types correspond to terminals
Values to contents of token read in
Examples
Int 549 integer token with value 549 read in
if - if keyword, no nee
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.243j (Fall 2003): DYNAMICS OF NONLINEAR SYSTEMS
by A. Megretski
Problem Set 5 Solutions1
Problem 5.1
y(t) a is an equilibrium solution of the differential eq