ELEN 239 Topics in System Theory: Fast Fourier Transforms and Their Applications
Course Description:
The Fast Fourier Transform (FFT) family of algorithms has
revolutionized
many areas of scientific and engineering computation. As rapid progress
of VLSI
technology continues, recent years have seen growing use of
more
and more
sophisticated FFT algorithms. For example, a leading 4G
cellular standard, endorsed by major carrier
s
such as Verizon and AT&T,
requires the use of mixed

radix DFT. This will make it
virtually certain
that any
4G
cellular phones
adopted
by these major carriers
in the near
future
must
have an implementation of the
advanced FFT algorithms. In
addition to the traditional radix

2 FFT algorithms, this course will cover
these advanced FFT a
lgorithm
s
which include
fast convolution algorithms
(Cook

Toom, and Winograd)
used in many mixed radix

FFT
,
a variety of
mixed radix FFT
s
(Cooley

Turkey, Agarwal

Cooley and Auto

Sort FFT
s
),
and
Prime Factor Algorithm
s
(PFA)
. We will also
cover
the quantiza
tion
effects of fixed point arithmetic on FFT algorithms
.
Expected outcomes:
Upon completing the course, the students should
1)
Understand the halving and doubling strategy, apply it in deriving the
radix

2 FFT algorithm and obtain a recursive implementatio
n using a
programming language of one’s choice.
2)
Understand the structure of radix

2FFT algorithm and be able to obtain
a non

recursive implementation
3)
Be able to use halving and doubling strategy to derive Cooley

Turkey
FFT algorithm and understand its stru
cture
4)
Be able to use Chinese remainder theorem to derive prime

factor FFT
algorithm and Winograd small FFT algorithms.
5)
Be able to combine the 3) and 4) to obtain an FFT algorithm of any
size. Be able to select the appropriate types of FFT algorithms based
on the application requirements and FFT algorithm knowledge
acquired in the course.
Course Prerequisite:
Familiarity with MATLAB or other high

level language, Fourier analysis,
and linear algebra. (2 units)
.
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