Math 320: Wavelet and Fourier analysis
Instructor |
Tanya Leise |
Email |
tleise at amherst dot edu |
Phone |
542-5411 |
Office |
SMudd 503 |
Office hours |
MWF 11am-noon
WTh 2-3:30pm
Other times by appointment or simply try stopping by my office |
Text |
Harmonic Analysis From Fourier to Wavelets by Peyeyra & Ward |
Course goals:
- Understand time-frequency analysis from at least two points of view: 1) expressing signals as a combination of basis elements, whether sinusoids or wavelets; 2)
transforming data from the time or space domain to a different domain, such as the frequency domain.
- Visualize how wavelets and Fourier analysis work by using software (Matlab) to explore applications.
Course Topics:
- Background on complex numbers and inner product spaces of functions
- Fourier series and Fourier transforms
-
Haar transform, a simple wavelet transform good for building intuition
- Multiresolution analysis of signals and images
- Daubechies wavelets
Attendance: You are
to be in class and to be there on time. Cooperative learning is more
effective
and more fun than struggling through material on your own.
If you do
miss a lecture, it is your responsibility to obtain the material that
you
missed and to get your assignments handed in to me.
Questions:
If you
have a question during lecture, please raise your hand and ask it right
away.
Chances are that other students are wondering the same thing. If a
question
arises later, feel free to visit my office and we'll work through
sample
problems until you are comfortable with the mathematics.
Always feel free to ask me to slow down
as well.
Grading: Your course grade will be based on class participation (10%), two midterm exams (50%), regular problem sets and labs (20%), and a final project
(20%).
Intellectual Responsibility
- Exams. Your work must be entirely your own, so
please follow the guidelines of the honor code. Unless I explicitly
allow other aids, you are only allowed whatever implements you need to
read and write (no notes or calculators). Please turn off your
cell phone in kindness to your fellow test-takers during in-class exams.
- Homework and labs. You may study with other students
following these guidelines:
- If you worked with or received help
from any source other than me, you should put a note on the front of
your homework saying, "I worked with <names>."
Make sure your name stands out as the author of your
homework.
- Working together does not mean that
one of you does the first half of the homework set and the other does
the second. Everyone should work on every problem.
- Each student must hand in his or her
own problem set. You may not hand in a single packet as the work of
multiple people.
You must do your own write-up of each problem.
- Do not copy someone else's
solution—you will not learn anything and it is plagiarism.
You may discuss problems with others, but then you must be
able to work out the solution on your own again and write it down
yourself.
- Sending or receiving a copy of a file that contains student work violates the honor code and will be treated as plagiarism. You may talk with others about strategies for solving a problem in Matlab, but please do not share files.
- If you are unsure what agrees or
does not agree with the precepts of intellectual responsibility in this
course, feel free to talk to me about it.
Homework Guidelines
- All problem sets are due at THE
START OF CLASS.
Late homework will receive half credit for homework handed
in after start of class but within 2 class days (e.g., homework due
Monday will get half-credit if handed in after the start of class on
Monday through Wednesday start of class, and will not accepted after
that).
- If you are unable to attend class due
to illness or an emergency, let me know as soon as you can and we will
work out an appropriate schedule for assignments.
- Your name should be written on all
sheets handed in.
- Problem solutions must be written out
in the order they were assigned.
- Multiple pages must be stapled or clipped together.
- Homework should be neat.
No dog ears. No messy edges
from notebook paper.
- Where appropriate, please box or
highlight final answers. In general, try
to make your answers readable and easy to find. Always
keep the grader happy!
- As mentioned elsewhere, no copying!
Course Resources:
Don't struggle alone! You have many options for
getting help
with this course.
- Me. Feel free to come to my office hours,
make an appointment by email or phone, or simply try stopping by my
office—you are welcome whenever my door is open. If
you have some anxiety about taking math exams, please come see me and
we can work together on building your math confidence.
- Homework. Although the practice problems are not
graded, please work through them. Mathematics
is learned ACTIVELY, not passively. You
can't absorb math through listening or reading, even if you think you
understand it all.
- Textbook. I won't go over everything that is
contained in the text, and I will try to avoid doing the same examples. Hence your textbook in an important
independent source of information and you should read it!
- Lecture notes. Reviewing the notes you take in lecture
will give you a chance to see the material again after you have had
some time to assimilate it.
- Your classmates. Discussing math with others can help you
think through the concepts. Explaining an
idea you already understand will deepen your comprehension, and for the
concepts that you don't understand well, the explanation of a peer may
be more helpful than mine or the textbook's.
- Library resources. There are a variety of books covering wavelets and/or Fourier analysis in the library that you may find it helpful to peruse, which can be very helpful if the textbook doesn't explain a topic in a way that makes sense to you or if you want to see some further examples.
To the Math 320 Homework Schedule