Supplementary Notes for ELEN 4810 Lecture 6
The Discrete Time Fourier Transform
John Wright
Columbia University
September 26, 2016
Disclaimer: These notes are intended to be an accessible introduction to the subject, with no pretense at completeness. In g
Supplementary Notes for ELEN 4810 Lecture 3
Introduction to Linear Time Invariant Systems
John Wright
Columbia University
September 14, 2016
Disclaimer: These notes are intended to be an accessible introduction to the subject, with no pretense at complete
Supplementary Notes for ELEN 4810 Lecture 4
More Linear Time Invariant Systems
John Wright
Columbia University
September 19, 2016
Disclaimer: These notes are intended to be an accessible introduction to the subject, with no pretense at completeness. In ge
Supplementary Notes for ELEN 4810 Lecture 2
Basic Signals and Operations
John Wright
Columbia University
September 12, 2016
Disclaimer: These notes are intended to be an accessible introduction to the subject, with no pretense at completeness. In general,
Supplementary Notes for ELEN 4810 Lecture 1
DT Signals + A Brief Review of Complex Arithmetic
John Wright
Columbia University
September 7, 2016
Disclaimer: These notes are intended to be an accessible introduction to the subject, with no pretense at compl
Supplementary Notes for ELEN 4810 Lecture 5
Review of Fourier Representations
John Wright
Columbia University
September 21, 2016
Disclaimer: These notes are intended to be an accessible introduction to the subject, with no pretense at completeness. In gen
ELEN4810 Digital Signal Processing
The goal of this course is to equip students with basic tools for processing signals on a computer.
We will introduce the basic mathematical ideas necessary to design and analyze discrete time systems, and interface them
ELEN 4810 Homework 2
Due Monday, October 3. Please submit your code for the computational section online via
Courseworks. You can submit your answers to the analytical question, as well as the output of your
code via one of three means:
 Hardcopy submiss
10 Vacuum Science and Plasmas
10.1) Since the pressure is ‘ ‘ ‘
still well \’lll1ln ’
. I, . ‘ the V18‘ ~ 
10.10 are still \alld. According to Equation [0 l lions “0W w
of pressure In this regime. The red . .
uction in temper
toward lower velocrties. Acc
Homework Assignment #3
Principals of Device Microfabrication
ELENE4944, Fall 2015
Due Date: 10/19/15 at the start of class.
Assignment: Problems 5.2, 5.5, 5.7, 5.10 of Chapter 5 and 6.2, 6.7 of the Chapter
5.2) From Figure 5.9, if RP = 300 nm, then the energy is about 90 keV. Then ARp = 68
nm. The dose can be found from the peak concentration as
N(x=R,)=lO”cm'3 =——£—, then
(0:427:*6.8*104’cm*10'7cm‘3=1.7*10”cm‘2
If the bulk is 1015 cm'3, then
MPG—IS]: —_._(
7. I) According to Equation 6.5,
A _ 0.2898 cm — K
in.“ _IT
* —() _
=2.898 10 nm K=]4,490 K
200 nm
The internal energy ol‘the gas is 3/2 * kT * N, where N is the number of atoms in the
vapor.
T
N=6.02 *10”“‘°ms& = 2.64 *102' atoms
mOIC
mole
Then the
Homework Assignment #4
Principals of Device Microfabrication
ELENE4944, Fall 2015
Due Date: 11/9/15 at the start of class.
Assignment: Problems 7.1, 7.4, 7.9, 8.2, 8.4, and 8.8 of the Chapter 7 and 8 of the 4th
Edition of the course text.
Homework Assignment #5
Principals of Device Microfabrication
ELENE4944, Fall 2015
Due Date: 11/16/15 at the start of class.
Assignment: Problems 16 of the Chapter 10 of the 4th Edition of the course text.
Note: Homework can be turned in at
Below are the solutions to examples for those who followed 3 rd Edition while solving Homework 2.
4.1 and 4.3 are same as 4th Edition
Solution for 4.5, 4.8 and 4.9 can be found below, which are 4.6, 4.9, 4.10 according to 4 th Edition,
respectively.
*4.5
3 Diffusion
3.1) One would need to measure the diffusivity as a function of temperature and then plot
the data as an Arrhenius function (log D vs. 1/ T). Ideally this should be done with various
doping concentrations to extract charge effects. If D is con
Principles of Communication Systems
1. Columbia University
2. ELEN E3701
Spring Semester 2016
Problem Set # 12
Problem Set Due:
3.
Problem # 1
You are given a binary communications system, using the two
signals shown below. Assume that the noise is addit
Principles of Communication Systems
Columbia University
ELEN E3701
Spring Semester 2016
Problem Set # 11
Problem Set Due:
Problem # 1 (This is a typical final exam problem!)
We have decided to use the following 32ary (five bits/symbol)
modulation techni
Principles of Communication Systems
Columbia University
ELEN E3701
Spring Semester 2016
Problem Set # 9
Problem Set Due:
Problem # 1
In class we discussed the use of optimum filtering for a binary
Nyquist PAM system using Nyquist signals with squareroot
Principles of Communication Systems
Columbia University
ELEN E3701
Spring Semester 2016
Problem Set # 10
Problem Set Due:
Problem # 1
a. Show that the general equation for the average energy per signal,
Es, of a square QAM constellation is given by
Es=[(
1
Principles of Communication
Systems
Columbia University
ELEN E3701
Spring Semester 2013
Midterm Examination
4 April 2013
Professor I. Kalet
Length of Examination One hour and
fifteen minutes
Answer both questions
Each question is worth 50 points
O
1
Principles of Communication
Systems
Columbia University
ELEN E3701
Spring Semester 2014
Midterm Examination
27 March 2014
Professor I. Kalet
Length of Examination One hour and
fifteen minutes
Answer both questions
Each question is worth 50 points

Principles of Communication
Systems
Columbia University
Professor 1. Kalet
0 Length of Examination— One hour and
ﬁfteen minutes
0 Answer both questions
6 Each question is worth 50 points
“Ones
mﬂpen Notes
ComnutermNﬂ Problem #1 150 Points!
This year w